Господин Экзамен
Общий знаменатель (-4-3*sin(x))/(2-5*x)+5*(3*cos(x)-4*x)/(2-5*x)^2
Решение
Вы ввели
[src]
-4 - 3*sin(x) 5*(3*cos(x) - 4*x)
------------- + ------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}} + \frac{- 3 \sin{\left(x \right)} - 4}{- 5 x + 2}$$
(-4 - 3*sin(x))/(2 - 5*x) + 5*(3*cos(x) - 4*x)/((2 - 5*x)^2)
Общее упрощение
[src]
-20*x + 15*cos(x) + (-2 + 5*x)*(4 + 3*sin(x))
---------------------------------------------
2
(-2 + 5*x)
$$\frac{\left(5 x - 2\right) \left(3 \sin{\left(x \right)} + 4\right) - 20 x + 15 \cos{\left(x \right)}}{\left(5 x - 2\right)^{2}}$$
(-20*x + 15*cos(x) + (-2 + 5*x)*(4 + 3*sin(x)))/(-2 + 5*x)^2
Рациональный знаменатель
[src]
4 20*x 3*sin(x) 15*cos(x)
- ------- - ---------- - -------- + ----------
2 - 5*x 2 2 - 5*x 2
(2 - 5*x) (2 - 5*x)
$$- \frac{3 \sin{\left(x \right)}}{- 5 x + 2} - \frac{20 x}{\left(- 5 x + 2\right)^{2}} - \frac{4}{- 5 x + 2} + \frac{15 \cos{\left(x \right)}}{\left(- 5 x + 2\right)^{2}}$$
2
(2 - 5*x) *(-4 - 3*sin(x)) + (2 - 5*x)*(-20*x + 15*cos(x))
----------------------------------------------------------
3
(2 - 5*x)
$$\frac{\left(- 5 x + 2\right)^{2} \left(- 3 \sin{\left(x \right)} - 4\right) + \left(- 5 x + 2\right) \left(- 20 x + 15 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{3}}$$
((2 - 5*x)^2*(-4 - 3*sin(x)) + (2 - 5*x)*(-20*x + 15*cos(x)))/(2 - 5*x)^3
Собрать выражение
[src]
-4 - 3*sin(x) 5*(-4*x + 3*cos(x))
------------- + -------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \sin{\left(x \right)} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
4 20*x 3*sin(x) 15*cos(x)
-------- - ---------------- + -------- + ----------------
-2 + 5*x 2 -2 + 5*x 2
4 - 20*x + 25*x 4 - 20*x + 25*x
$$- \frac{20 x}{25 x^{2} - 20 x + 4} + \frac{15 \cos{\left(x \right)}}{25 x^{2} - 20 x + 4} + \frac{3 \sin{\left(x \right)}}{5 x - 2} + \frac{4}{5 x - 2}$$
4/(-2 + 5*x) - 20*x/(4 - 20*x + 25*x^2) + 3*sin(x)/(-2 + 5*x) + 15*cos(x)/(4 - 20*x + 25*x^2)
Общий знаменатель
[src]
-8 - 6*sin(x) + 15*cos(x) + 15*x*sin(x)
---------------------------------------
2
4 - 20*x + 25*x
$$\frac{15 x \sin{\left(x \right)} - 6 \sin{\left(x \right)} + 15 \cos{\left(x \right)} - 8}{25 x^{2} - 20 x + 4}$$
(-8 - 6*sin(x) + 15*cos(x) + 15*x*sin(x))/(4 - 20*x + 25*x^2)
Объединение рациональных выражений
[src]
-20*x + 15*cos(x) + (-4 - 3*sin(x))*(2 - 5*x)
---------------------------------------------
2
(2 - 5*x)
$$\frac{\left(- 5 x + 2\right) \left(- 3 \sin{\left(x \right)} - 4\right) - 20 x + 15 \cos{\left(x \right)}}{\left(- 5 x + 2\right)^{2}}$$
(-20*x + 15*cos(x) + (-4 - 3*sin(x))*(2 - 5*x))/(2 - 5*x)^2
Комбинаторика
[src]
-8 - 6*sin(x) + 15*cos(x) + 15*x*sin(x)
---------------------------------------
2
(-2 + 5*x)
$$\frac{15 x \sin{\left(x \right)} - 6 \sin{\left(x \right)} + 15 \cos{\left(x \right)} - 8}{\left(5 x - 2\right)^{2}}$$
(-8 - 6*sin(x) + 15*cos(x) + 15*x*sin(x))/(-2 + 5*x)^2
Степени
[src]
-4 - 3*sin(x) -20*x + 15*cos(x)
------------- + -----------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \sin{\left(x \right)} - 4}{- 5 x + 2} + \frac{- 20 x + 15 \cos{\left(x \right)}}{\left(- 5 x + 2\right)^{2}}$$
-4 - 3*sin(x) 5*(-4*x + 3*cos(x))
------------- + -------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \sin{\left(x \right)} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ -I*x I*x\ / I*x -I*x\
3*I*\- e + e / | 3*e 3*e |
-4 + -------------------- 5*|-4*x + ------ + -------|
2 \ 2 2 /
------------------------- + ---------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{\frac{3 i \left(e^{i x} - e^{- i x}\right)}{2} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 e^{i x}}{2} + \frac{3 e^{- i x}}{2}\right)}{\left(- 5 x + 2\right)^{2}}$$
(-4 + 3*i*(-exp(-i*x) + exp(i*x))/2)/(2 - 5*x) + 5*(-4*x + 3*exp(i*x)/2 + 3*exp(-i*x)/2)/(2 - 5*x)^2
Тригонометрическая часть
[src]
-4 - 3*sin(x) -20*x + 15*cos(x)
------------- + -----------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \sin{\left(x \right)} - 4}{- 5 x + 2} + \frac{- 20 x + 15 \cos{\left(x \right)}}{\left(- 5 x + 2\right)^{2}}$$
4 + 3*sin(x) 5*(-4*x + 3*cos(x))
- ------------ + -------------------
2 - 5*x 2
(2 - 5*x)
$$- \frac{3 \sin{\left(x \right)} + 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
-4 - 3*sin(x) 5*(-4*x + 3*cos(x))
------------- + -------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \sin{\left(x \right)} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
3 / 3 \
-4 - ------ 5*|-4*x + ------|
csc(x) \ sec(x)/
----------- + -----------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{3}{\csc{\left(x \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3}{\sec{\left(x \right)}}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ / pi\\
5*|-4*x + 3*sin|x + --||
4 + 3*sin(x) \ \ 2 //
- ------------ + ------------------------
2 - 5*x 2
(2 - 5*x)
$$- \frac{3 \sin{\left(x \right)} + 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \sin{\left(x + \frac{\pi}{2} \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ pi\
4 + 3*cos|x - --|
\ 2 / 5*(-4*x + 3*cos(x))
- ----------------- + -------------------
2 - 5*x 2
(2 - 5*x)
$$- \frac{3 \cos{\left(x - \frac{\pi}{2} \right)} + 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ / pi\\
5*|-4*x + 3*sin|x + --||
-4 - 3*sin(x) \ \ 2 //
------------- + ------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \sin{\left(x \right)} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \sin{\left(x + \frac{\pi}{2} \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ pi\
-4 - 3*cos|x - --|
\ 2 / 5*(-4*x + 3*cos(x))
------------------ + -------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \cos{\left(x - \frac{\pi}{2} \right)} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
3
-4 - -----------
/ pi\ / 3 \
sec|x - --| 5*|-4*x + ------|
\ 2 / \ sec(x)/
---------------- + -----------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{3}{\sec{\left(x - \frac{\pi}{2} \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3}{\sec{\left(x \right)}}\right)}{\left(- 5 x + 2\right)^{2}}$$
3
4 + -----------
/ pi\ / 3 \
sec|x - --| 5*|-4*x + ------|
\ 2 / \ sec(x)/
- --------------- + -----------------
2 - 5*x 2
(2 - 5*x)
$$- \frac{4 + \frac{3}{\sec{\left(x - \frac{\pi}{2} \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3}{\sec{\left(x \right)}}\right)}{\left(- 5 x + 2\right)^{2}}$$
3
-4 - -----------
/pi \ / 3 \
sec|-- - x| 5*|-4*x + ------|
\2 / \ sec(x)/
---------------- + -----------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{3}{\sec{\left(- x + \frac{\pi}{2} \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3}{\sec{\left(x \right)}}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ 3 \
5*|-4*x + -----------|
3 | /pi \|
-4 - ------ | csc|-- - x||
csc(x) \ \2 //
----------- + ----------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{3}{\csc{\left(x \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ 3 \
5*|-4*x + -----------|
3 | /pi \|
4 + ------ | csc|-- - x||
csc(x) \ \2 //
- ---------- + ----------------------
2 - 5*x 2
(2 - 5*x)
$$- \frac{4 + \frac{3}{\csc{\left(x \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ 3 \
5*|-4*x + -----------|
3 | /pi \|
-4 - ----------- | csc|-- - x||
csc(pi - x) \ \2 //
---------------- + ----------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{3}{\csc{\left(- x + \pi \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)}{\left(- 5 x + 2\right)^{2}}$$
/x\
-4 - 3*(1 + cos(x))*tan|-|
\2/ 5*(-4*x + 3*cos(x))
-------------------------- + -------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- 3 \left(\cos{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ 2/x pi\\
3*|1 - cot |- + --||*(1 + sin(x))
\ \2 4 //
-4 - ---------------------------------
2 5*(-4*x + 3*cos(x))
-------------------------------------- + -------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- \frac{3 \cdot \left(- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(x \right)} + 1\right)}{2} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
2/x\
12*sin |-|*sin(x)
\2/
-4 - -------------------
2 4/x\
sin (x) + 4*sin |-|
\2/ 5*(-4*x + 3*cos(x))
------------------------ + -------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- \frac{12 \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)} + \sin^{2}{\left(x \right)}} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + 3 \cos{\left(x \right)}\right)}{\left(- 5 x + 2\right)^{2}}$$
/x\ / / 2/x\\\
6*tan|-| | 3*|1 - tan |-|||
\2/ | \ \2//|
-4 - ----------- 5*|-4*x + ---------------|
2/x\ | 2/x\ |
1 + tan |-| | 1 + tan |-| |
\2/ \ \2/ /
---------------- + --------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{6 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \cdot \left(- \tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
/x\ / / 2/x\\\
6*tan|-| | 3*|1 - tan |-|||
\2/ | \ \2//|
4 + ----------- 5*|-4*x + ---------------|
2/x\ | 2/x\ |
1 + tan |-| | 1 + tan |-| |
\2/ \ \2/ /
- --------------- + --------------------------
2 - 5*x 2
(2 - 5*x)
$$- \frac{4 + \frac{6 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \cdot \left(- \tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
/x\ / /x pi\ \
6*tan|-| | 6*tan|- + --| |
\2/ | \2 4 / |
-4 - ----------- 5*|-4*x + ----------------|
2/x\ | 2/x pi\|
1 + tan |-| | 1 + tan |- + --||
\2/ \ \2 4 //
---------------- + ---------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{6 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{6 \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
/x\ / /x pi\ \
6*cot|-| | 6*tan|- + --| |
\2/ | \2 4 / |
-4 - ----------- 5*|-4*x + ----------------|
2/x\ | 2/x pi\|
1 + cot |-| | 1 + tan |- + --||
\2/ \ \2 4 //
---------------- + ---------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{6 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{6 \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ / 1 \\
| 3*|1 - -------||
| | 2/x\||
| | cot |-|||
6 | \ \2//|
-4 - -------------------- 5*|-4*x + ---------------|
/ 1 \ /x\ | 1 |
|1 + -------|*cot|-| | 1 + ------- |
| 2/x\| \2/ | 2/x\ |
| cot |-|| | cot |-| |
\ \2// \ \2/ /
------------------------- + --------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{6}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \cot{\left(\frac{x}{2} \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \cdot \left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)}{1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ 2/x pi\\ / / 2/x\\\
3*|-1 + tan |- + --|| | 3*|-1 + cot |-|||
\ \2 4 // | \ \2//|
-4 - --------------------- 5*|-4*x + ----------------|
2/x pi\ | 2/x\ |
1 + tan |- + --| | 1 + cot |-| |
\2 4 / \ \2/ /
-------------------------- + ---------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- \frac{3 \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1\right)}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ 2/x pi\\ / / 2/x\\\
3*|1 - cot |- + --|| | 3*|1 - tan |-|||
\ \2 4 // | \ \2//|
-4 - -------------------- 5*|-4*x + ---------------|
2/x pi\ | 2/x\ |
1 + cot |- + --| | 1 + tan |-| |
\2 4 / \ \2/ /
------------------------- + --------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{- \frac{3 \cdot \left(- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right)}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} - 4}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \cdot \left(- \tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
// 0 for x mod pi = 0\ // 1 for x mod 2*pi = 0\
4 + 3*|< | -20*x + 15*|< |
\\sin(x) otherwise / \\cos(x) otherwise /
--------------------------------- + ----------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// 1 for x mod 2*pi = 0\
|| |
// 0 for x mod pi = 0\ -20*x + 15*|< / pi\ |
4 + 3*|< | ||sin|x + --| otherwise |
\\sin(x) otherwise / \\ \ 2 / /
--------------------------------- + ---------------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\sin{\left(x + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\
|| |
4 + 3*|< / pi\ | // 1 for x mod 2*pi = 0\
||cos|x - --| otherwise | -20*x + 15*|< |
\\ \ 2 / / \\cos(x) otherwise /
-------------------------------------- + ----------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\cos{\left(x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// / 3*pi\ \
|| 1 for |x + ----| mod 2*pi = 0|
4 + 3*|< \ 2 / | // 1 for x mod 2*pi = 0\
|| | -20*x + 15*|< |
\\sin(x) otherwise / \\cos(x) otherwise /
-------------------------------------------- + ----------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\
|| |
|| 1 | // 1 for x mod 2*pi = 0\
4 + 3*|<----------- otherwise | || |
|| / pi\ | -20*x + 15*|< 1 |
||sec|x - --| | ||------ otherwise |
\\ \ 2 / / \\sec(x) /
-------------------------------------- + ----------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(x \right)}} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// 1 for x mod 2*pi = 0\
|| |
// 0 for x mod pi = 0\ || 1 |
|| | -20*x + 15*|<----------- otherwise |
4 + 3*|< 1 | || /pi \ |
||------ otherwise | ||csc|-- - x| |
\\csc(x) / \\ \2 / /
--------------------------------- + ---------------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{\csc{\left(x \right)}} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\
|| |
||1 - cos(x) |
4 + 3*|<---------- otherwise |
|| /x\ | // 1 for x mod 2*pi = 0\
|| tan|-| | -20*x + 15*|< |
\\ \2/ / \\cos(x) otherwise /
------------------------------------- + ----------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{- \cos{\left(x \right)} + 1}{\tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
/ / 4/x\\\
| | 4*sin |-|||
| | \2/||
2/x\ | 3*|1 - ---------||
12*sin |-| | | 2 ||
\2/ | \ sin (x) /|
-4 - ---------------------- 5*|-4*x + -----------------|
/ 4/x\\ | 4/x\ |
| 4*sin |-|| | 4*sin |-| |
| \2/| | \2/ |
|1 + ---------|*sin(x) | 1 + --------- |
| 2 | | 2 |
\ sin (x) / \ sin (x) /
--------------------------- + ----------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{12 \sin^{2}{\left(\frac{x}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin{\left(x \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)}{\frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
// / pi\ \
|| 0 for |x + --| mod pi = 0|
|| \ 2 / |
|| |
-20*x + 15*|< 1 + sin(x) |
||----------- otherwise |
// 0 for x mod pi = 0\ || /x pi\ |
4 + 3*|< | ||tan|- + --| |
\\sin(x) otherwise / \\ \2 4 / /
--------------------------------- + --------------------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 0 & \text{for}\: \left(x + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{\sin{\left(x \right)} + 1}{\tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\ // 1 for x mod 2*pi = 0\
|| | || |
|| /x\ | || 2/x\ |
|| 2*tan|-| | ||1 - tan |-| |
4 + 3*|< \2/ | -20*x + 15*|< \2/ |
||----------- otherwise | ||----------- otherwise |
|| 2/x\ | || 2/x\ |
||1 + tan |-| | ||1 + tan |-| |
\\ \2/ / \\ \2/ /
-------------------------------------- + ---------------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{x}{2} \right)} + 1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\ / // 1 for x mod 2*pi = 0\\
|| | | || ||
|| /x\ | | || 2/x\ ||
|| 2*cot|-| | | ||-1 + cot |-| ||
-4 - 3*|< \2/ | 5*|-4*x + 3*|< \2/ ||
||----------- otherwise | | ||------------ otherwise ||
|| 2/x\ | | || 2/x\ ||
||1 + cot |-| | | ||1 + cot |-| ||
\\ \2/ / \ \\ \2/ //
--------------------------------------- + ------------------------------------------------
2 - 5*x 2
(2 - 5*x)
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\ / // 1 for x mod 2*pi = 0\\
|| | | || ||
|| /x\ | | || 2/x\ ||
|| 2*cot|-| | | ||-1 + cot |-| ||
4 + 3*|< \2/ | 5*|-4*x + 3*|< \2/ ||
||----------- otherwise | | ||------------ otherwise ||
|| 2/x\ | | || 2/x\ ||
||1 + cot |-| | | ||1 + cot |-| ||
\\ \2/ / \ \\ \2/ //
- -------------------------------------- + ------------------------------------------------
2 - 5*x 2
(2 - 5*x)
$$\left(- \frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
/ / 2/x\ \\
| | sec |-| ||
| | \2/ ||
| 3*|1 - ------------||
/x\ | | 2/x pi\||
6*sec|-| | | sec |- - --|||
\2/ | \ \2 2 //|
-4 - ------------------------------ 5*|-4*x + --------------------|
/ 2/x\ \ | 2/x\ |
| sec |-| | | sec |-| |
| \2/ | /x pi\ | \2/ |
|1 + ------------|*sec|- - --| | 1 + ------------ |
| 2/x pi\| \2 2 / | 2/x pi\ |
| sec |- - --|| | sec |- - --| |
\ \2 2 // \ \2 2 / /
----------------------------------- + -------------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{6 \sec{\left(\frac{x}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)}{\frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ / 2/x pi\\\
| | cos |- - --|||
| | \2 2 /||
| 3*|1 - ------------||
/x pi\ | | 2/x\ ||
6*cos|- - --| | | cos |-| ||
\2 2 / | \ \2/ /|
-4 - ------------------------- 5*|-4*x + --------------------|
/ 2/x pi\\ | 2/x pi\ |
| cos |- - --|| | cos |- - --| |
| \2 2 /| /x\ | \2 2 / |
|1 + ------------|*cos|-| | 1 + ------------ |
| 2/x\ | \2/ | 2/x\ |
| cos |-| | | cos |-| |
\ \2/ / \ \2/ /
------------------------------ + -------------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{6 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos{\left(\frac{x}{2} \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \cdot \left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right)}{1 + \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}}\right)}{\left(- 5 x + 2\right)^{2}}$$
// 0 for x mod pi = 0\ // 1 for x mod 2*pi = 0\
|| | || |
4 + 3*|
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
/ / 2/pi x\\\
| | csc |-- - -|||
| | \2 2/||
| 3*|1 - ------------||
/pi x\ | | 2/x\ ||
6*csc|-- - -| | | csc |-| ||
\2 2/ | \ \2/ /|
-4 - ------------------------- 5*|-4*x + --------------------|
/ 2/pi x\\ | 2/pi x\ |
| csc |-- - -|| | csc |-- - -| |
| \2 2/| /x\ | \2 2/ |
|1 + ------------|*csc|-| | 1 + ------------ |
| 2/x\ | \2/ | 2/x\ |
| csc |-| | | csc |-| |
\ \2/ / \ \2/ /
------------------------------ + -------------------------------
2 - 5*x 2
(2 - 5*x)
$$\frac{-4 - \frac{6 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)}}}{- 5 x + 2} + \frac{5 \left(- 4 x + \frac{3 \cdot \left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)}{1 + \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}}\right)}{\left(- 5 x + 2\right)^{2}}$$
/ // 1 for x mod 2*pi = 0\\
| || ||
| || 1 ||
| ||-1 + ------- ||
// 0 for x mod pi = 0\ | || 2/x\ ||
|| | | || tan |-| ||
|| 2 | 5*|-4*x + 3*|< \2/ ||
||-------------------- otherwise | | ||------------ otherwise ||
-4 - 3*|
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
/ // / pi\ \\
| || 0 for |x + --| mod pi = 0||
// 0 for x mod pi = 0\ | || \ 2 / ||
|| | | || ||
|| /x\ | | || /x pi\ ||
|| 2*cot|-| | 5*|-4*x + 3*|< 2*cot|- + --| ||
-4 - 3*|< \2/ | | || \2 4 / ||
||----------- otherwise | | ||---------------- otherwise ||
|| 2/x\ | | || 2/x pi\ ||
||1 + cot |-| | | ||1 + cot |- + --| ||
\\ \2/ / \ \\ \2 4 / //
--------------------------------------- + ---------------------------------------------------------
2 - 5*x 2
(2 - 5*x)
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 0 & \text{for}\: \left(x + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
// / 3*pi\ \
|| 1 for |x + ----| mod 2*pi = 0|
|| \ 2 / | / // 1 for x mod 2*pi = 0\\
|| | | || ||
|| 2/x pi\ | | || 2/x\ ||
-4 - 3*|<-1 + tan |- + --| | | ||-1 + cot |-| ||
|| \2 4 / | 5*|-4*x + 3*|< \2/ ||
||----------------- otherwise | | ||------------ otherwise ||
|| 2/x pi\ | | || 2/x\ ||
|| 1 + tan |- + --| | | ||1 + cot |-| ||
\\ \2 4 / / \ \\ \2/ //
-------------------------------------------------------- + ------------------------------------------------
2 - 5*x 2
(2 - 5*x)
$$\left(\frac{\left(- 3 \left(\begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\
|| |
|| 2*sin(x) |
||---------------------------- otherwise |
|| / 2 \ | / // 1 for x mod 2*pi = 0\\
-4 - 3*|< | sin (x) | | | || ||
||(1 - cos(x))*|1 + ---------| | | || 2 ||
|| | 4/x\| | 5*|-4*x + 3*|< -4 + 4*sin (x) + 4*cos(x) ||
|| | 4*sin |-|| | | ||--------------------------- otherwise ||
|| \ \2// | | || 2 2 ||
\\ / \ \\2*(1 - cos(x)) + 2*sin (x) //
-------------------------------------------------------- + ---------------------------------------------------------------
2 - 5*x 2
(2 - 5*x)
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \left(- \cos{\left(x \right)} + 1\right)} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{4 \sin^{2}{\left(x \right)} + 4 \cos{\left(x \right)} - 4}{2 \left(- \cos{\left(x \right)} + 1\right)^{2} + 2 \sin^{2}{\left(x \right)}} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
// 0 for x mod pi = 0\ // 1 for x mod 2*pi = 0\
|| | || |
||/ 0 for x mod pi = 0 | ||/ 1 for x mod 2*pi = 0 |
||| | ||| |
||| /x\ | ||| 2/x\ |
4 + 3*|<| 2*cot|-| | -20*x + 15*|<|-1 + cot |-| |
||< \2/ otherwise | ||< \2/ otherwise |
|||----------- otherwise | |||------------ otherwise |
||| 2/x\ | ||| 2/x\ |
|||1 + cot |-| | |||1 + cot |-| |
\\\ \2/ / \\\ \2/ /
--------------------------------------------------------- + -------------------------------------------------------------------
-2 + 5*x 2
(-2 + 5*x)
$$\left(\frac{\left(3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 4}{5 x - 2}\right) + \left(\frac{- 20 x + \left(15 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)}{\left(5 x - 2\right)^{2}}\right)$$
/ // 1 for x mod 2*pi = 0\\
| || ||
| || 2 ||
| || sin (x) ||
// 0 for x mod pi = 0\ | ||-1 + --------- ||
|| | | || 4/x\ ||
|| sin(x) | | || 4*sin |-| ||
||----------------------- otherwise | 5*|-4*x + 3*|< \2/ ||
||/ 2 \ | | ||-------------- otherwise ||
-4 - 3*|<| sin (x) | 2/x\ | | || 2 ||
|||1 + ---------|*sin |-| | | || sin (x) ||
||| 4/x\| \2/ | | ||1 + --------- ||
||| 4*sin |-|| | | || 4/x\ ||
||\ \2// | | || 4*sin |-| ||
\\ / \ \\ \2/ //
--------------------------------------------------- + --------------------------------------------------
2 - 5*x 2
(2 - 5*x)
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{\sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}}{1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
/ // 1 for x mod 2*pi = 0\\
| || ||
| || 2/x\ ||
| || cos |-| ||
// 0 for x mod pi = 0\ | || \2/ ||
|| | | ||-1 + ------------ ||
|| /x\ | | || 2/x pi\ ||
|| 2*cos|-| | | || cos |- - --| ||
|| \2/ | 5*|-4*x + 3*|< \2 2 / ||
||------------------------------ otherwise | | ||----------------- otherwise ||
-4 - 3*|
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
/ // 1 for x mod 2*pi = 0\\
| || ||
| || 2/x pi\ ||
| || sec |- - --| ||
// 0 for x mod pi = 0\ | || \2 2 / ||
|| | | ||-1 + ------------ ||
|| /x pi\ | | || 2/x\ ||
|| 2*sec|- - --| | | || sec |-| ||
|| \2 2 / | 5*|-4*x + 3*|< \2/ ||
||------------------------- otherwise | | ||----------------- otherwise ||
-4 - 3*|
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right) \sec{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
/ // 1 for x mod 2*pi = 0\\
| || ||
| || 2/x\ ||
| || csc |-| ||
// 0 for x mod pi = 0\ | || \2/ ||
|| | | ||-1 + ------------ ||
|| /x\ | | || 2/pi x\ ||
|| 2*csc|-| | | || csc |-- - -| ||
|| \2/ | 5*|-4*x + 3*|< \2 2/ ||
||------------------------------ otherwise | | ||----------------- otherwise ||
-4 - 3*|
$$\left(\frac{\left(- 3 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{x}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - 4}{- 5 x + 2}\right) + \left(\frac{5 \left(- 4 x + \left(3 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)\right)\right)}{\left(- 5 x + 2\right)^{2}}\right)$$
(-4 - 3*Piecewise((0, Mod(x = pi, 0)), (2*csc(x/2)/((1 + csc(x/2)^2/csc(pi/2 - x/2)^2)*csc(pi/2 - x/2)), True)))/(2 - 5*x) + 5*(-4*x + 3*Piecewise((1, Mod(x = 2*pi, 0)), ((-1 + csc(x/2)^2/csc(pi/2 - x/2)^2)/(1 + csc(x/2)^2/csc(pi/2 - x/2)^2), True)))/(2 - 5*x)^2
Численный ответ
[src]
(-4.0 - 3.0*sin(x))/(2.0 - 5.0*x) + 0.2*(3.0*cos(x) - 4.0*x)/(0.4 - x)^2
(-4.0 - 3.0*sin(x))/(2.0 - 5.0*x) + 0.2*(3.0*cos(x) - 4.0*x)/(0.4 - x)^2