Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- p^3+8*p^2+7*p+32/5 если p=3/2
- 6*sin(6*x)-4^acot(x)*log(4)/(1+x^2) если x=-1/3
- x-7 если x=4
- 13*d*4 если d=1
- Разложить многочлен на множители:
- 18*x*y-6*x^2
- x^3-3*x^2-4*x+12
- 3*x^2+12*x+13
- x^3+2*x^2-4*x-8
- Общий знаменатель:
- (c^2-10*c+25)/(2*c+4)*(4*c+8)/(c^2-25)+2/(c+5)
- 36/a^2+3*a-12/a
- (y/4*y+16)-(y^2+16/4*y^2-64)-(4/y^2-4*y)
- (x-2/9+1/81*x)/(x-1/81*x)
- Умножение столбиком:
- 750*71
- 482*257
- 725*273
- 188*156
- Деление столбиком:
- 1050/4
- 389/6
- 3360/6
- 4736/6
- Раскрыть скобки в:
- n*(n+1)*(n+2)*(n+3)+1
- 243*3^(-3)
- (3*m-a)*(a+3*m)-(2*a+m)*(3*a-m)
- z*(12-x)
- Разложение числа на простые множители:
- 99358
- 4386
- 42056
- 29400
- Производная:
- -1/3
- Интеграл d{x}:
-
-1/3
-
Идентичные выражения
- шесть *sin(шесть *x)- четыре ^acot(x)*log(четыре)/(один +x^ два) если x=- один / три
- 6 умножить на синус от (6 умножить на x) минус 4 в степени арккотангенс от (x) умножить на логарифм от (4) делить на (1 плюс x в квадрате ) если x равно минус 1 делить на 3
- шесть умножить на синус от (шесть умножить на x) минус четыре в степени арккотангенс от (x) умножить на логарифм от (четыре) делить на (один плюс x в степени два) если x равно минус один делить на три
- 6*sin(6*x)-4acot(x)*log(4)/(1+x2) если x=-1/3
- 6*sin6*x-4acotx*log4/1+x2 если x=-1/3
- 6*sin(6*x)-4^acot(x)*log(4)/(1+x²) если x=-1/3
- 6*sin(6*x)-4 в степени acot(x)*log(4)/(1+x в степени 2) если x=-1/3
- 6sin(6x)-4^acot(x)log(4)/(1+x^2) если x=-1/3
- 6sin(6x)-4acot(x)log(4)/(1+x2) если x=-1/3
- 6sin6x-4acotxlog4/1+x2 если x=-1/3
- 6sin6x-4^acotxlog4/1+x^2 если x=-1/3
- 6*sin(6*x)-4^acot(x)*log(4)/(1+x^2) при x=-1/3
- 6*sin(6*x)-4^acot(x)*log(4) разделить на (1+x^2) если x=-1 разделить на 3
-
Похожие выражения
- 6*sin(6*x)+4^acot(x)*log(4)/(1+x^2) если x=-1/3
- 6*sin(6*x)-4^acot(x)*log(4)/(1+x^2) если x=+1/3
- 6*sin(6*x)-4^acot(x)*log(4)/(1-x^2) если x=-1/3
- 6*sin(6*x)-4^arccot(x)*log(4)/(1+x^2) если x=-1/3
- 6*sin(6*x)-4^arccotx*log(4)/(1+x^2) если x=-1/3
6*sin(6*x)-4^acot(x)*log(4)/(1+x^2) если x=-1/3
Решение
Вы ввели
[src]
acot(x)
4 *log(4)
6*sin(6*x) - ---------------
2
1 + x
$$6 \sin{\left(6 x \right)} - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
6*sin(6*x) - 4^acot(x)*log(4)/(1 + x^2)
Общее упрощение
[src]
/ 2\ acot(x)
\6 + 6*x /*sin(6*x) - 4 *log(4)
-------------------------------------
2
1 + x
$$\frac{\left(6 x^{2} + 6\right) \sin{\left(6 x \right)} - 4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
((6 + 6*x^2)*sin(6*x) - 4^acot(x)*log(4))/(1 + x^2)
Подстановка условия
[src]
6*sin(6*x) - 4^acot(x)*log(4)/(1 + x^2) при x = -1/3
подставляем
acot(x)
4 *log(4)
6*sin(6*x) - ---------------
2
1 + x
$$6 \sin{\left(6 x \right)} - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
/ 2\ acot(x)
\6 + 6*x /*sin(6*x) - 4 *log(4)
-------------------------------------
2
1 + x
$$\frac{\left(6 x^{2} + 6\right) \sin{\left(6 x \right)} - 4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
переменные
x = -1/3
$$x = - \frac{1}{3}$$
/ 2\ acot((-1/3))
\6 + 6*(-1/3) /*sin(6*(-1/3)) - 4 *log(4)
----------------------------------------------------
2
1 + (-1/3)
$$\frac{\left(6 (-1/3)^{2} + 6\right) \sin{\left(6 (-1/3) \right)} - 4^{\operatorname{acot}{\left((-1/3) \right)}} \log{\left(4 \right)}}{(-1/3)^{2} + 1}$$
/ 2\ acot(-1/3)
\6 + 6*-1/3 /*sin(6*-1/3) - 4 *log(4)
----------------------------------------------
2
1 + -1/3
$$\frac{\left(6 \left(- \frac{1}{3}\right)^{2} + 6\right) \sin{\left(6 \left(- \frac{1}{3}\right) \right)} - \frac{\log{\left(4 \right)}}{4^{- \operatorname{acot}{\left(- \frac{1}{3} \right)}}}}{\left(- \frac{1}{3}\right)^{2} + 1}$$
-acot(1/3)
9*4 *log(4)
-6*sin(2) - --------------------
10
$$- 6 \sin{\left(2 \right)} - \frac{9 \log{\left(4 \right)}}{10 \cdot 4^{\operatorname{acot}{\left(\frac{1}{3} \right)}}}$$
-6*sin(2) - 9*log(4)/(10*4^acot(1/3))
Численный ответ
[src]
6.0*sin(6*x) - 1.38629436111989*4.0^acot(x)/(1.0 + x^2)
6.0*sin(6*x) - 1.38629436111989*4.0^acot(x)/(1.0 + x^2)
Объединение рациональных выражений
[src]
acot(x) / 2\
- 4 *log(4) + 6*\1 + x /*sin(6*x)
---------------------------------------
2
1 + x
$$\frac{6 \left(x^{2} + 1\right) \sin{\left(6 x \right)} - 4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
(-4^acot(x)*log(4) + 6*(1 + x^2)*sin(6*x))/(1 + x^2)
Общий знаменатель
[src]
acot(x)
2*4 *log(2)
6*sin(6*x) - -----------------
2
1 + x
$$6 \sin{\left(6 x \right)} - \frac{2 \cdot 4^{\operatorname{acot}{\left(x \right)}} \log{\left(2 \right)}}{x^{2} + 1}$$
6*sin(6*x) - 2*4^acot(x)*log(2)/(1 + x^2)
Рациональный знаменатель
[src]
acot(x) / 2\
- 4 *log(4) + 6*\1 + x /*sin(6*x)
---------------------------------------
2
1 + x
$$\frac{6 \left(x^{2} + 1\right) \sin{\left(6 x \right)} - 4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
(-4^acot(x)*log(4) + 6*(1 + x^2)*sin(6*x))/(1 + x^2)
Степени
[src]
2*acot(x)
2 *log(4)
6*sin(6*x) - -----------------
2
1 + x
$$- \frac{2^{2 \operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + 6 \sin{\left(6 x \right)}$$
acot(x)
/ -6*I*x 6*I*x\ 4 *log(4)
- 3*I*\- e + e / - ---------------
2
1 + x
$$- 3 i \left(e^{6 i x} - e^{- 6 i x}\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
-3*i*(-exp(-6*i*x) + exp(6*i*x)) - 4^acot(x)*log(4)/(1 + x^2)
Комбинаторика
[src]
/ acot(x) 2 \
2*\3*sin(6*x) - 4 *log(2) + 3*x *sin(6*x)/
------------------------------------------------
2
1 + x
$$\frac{2 \left(3 x^{2} \sin{\left(6 x \right)} - 4^{\operatorname{acot}{\left(x \right)}} \log{\left(2 \right)} + 3 \sin{\left(6 x \right)}\right)}{x^{2} + 1}$$
2*(3*sin(6*x) - 4^acot(x)*log(2) + 3*x^2*sin(6*x))/(1 + x^2)
Собрать выражение
[src]
/ 2\ acot(x)
\6 + 6*x /*sin(6*x) - 4 *log(4)
-------------------------------------
2
1 + x
$$\frac{\left(6 x^{2} + 6\right) \sin{\left(6 x \right)} - 4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
((6 + 6*x^2)*sin(6*x) - 4^acot(x)*log(4))/(1 + x^2)
Тригонометрическая часть
[src]
acot(x)
6 4 *log(4)
-------- - ---------------
csc(6*x) 2
1 + x
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{6}{\csc{\left(6 x \right)}}$$
acot(x)
/ pi\ 4 *log(4)
6*cos|6*x - --| - ---------------
\ 2 / 2
1 + x
$$6 \cos{\left(6 x - \frac{\pi}{2} \right)} - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
acot(x)
6 4 *log(4)
------------- - ---------------
csc(pi - 6*x) 2
1 + x
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{6}{\csc{\left(- 6 x + \pi \right)}}$$
/ 2\ acot(x)
\6 + 6*x /*sin(6*x) - 4 *log(4)
-------------------------------------
2
1 + x
$$\frac{\left(6 x^{2} + 6\right) \sin{\left(6 x \right)} - 4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
acot(x)
4 *log(4)
12*cos(3*x)*sin(3*x) - ---------------
2
1 + x
$$12 \sin{\left(3 x \right)} \cos{\left(3 x \right)} - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
acot(x)
6 4 *log(4)
------------- - ---------------
/ pi\ 2
sec|6*x - --| 1 + x
\ 2 /
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{6}{\sec{\left(6 x - \frac{\pi}{2} \right)}}$$
acot(x)
6 4 *log(4)
------------- - ---------------
/pi \ 2
sec|-- - 6*x| 1 + x
\2 /
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{6}{\sec{\left(- 6 x + \frac{\pi}{2} \right)}}$$
acot(x)
12*tan(3*x) 4 *log(4)
------------- - ---------------
2 2
1 + tan (3*x) 1 + x
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{12 \tan{\left(3 x \right)}}{\tan^{2}{\left(3 x \right)} + 1}$$
acot(x)
12*cot(3*x) 4 *log(4)
------------- - ---------------
2 2
1 + cot (3*x) 1 + x
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{12 \cot{\left(3 x \right)}}{\cot^{2}{\left(3 x \right)} + 1}$$
acot(x)
12 4 *log(4)
------------------------ - ---------------
/ 1 \ 2
|1 + ---------|*cot(3*x) 1 + x
| 2 |
\ cot (3*x)/
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{12}{\left(1 + \frac{1}{\cot^{2}{\left(3 x \right)}}\right) \cot{\left(3 x \right)}}$$
acot(x)
/ 2/ pi\\ 4 *log(4)
3*|1 - cot |3*x + --||*(1 + sin(6*x)) - ---------------
\ \ 4 // 2
1 + x
$$3 \cdot \left(- \cot^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(6 x \right)} + 1\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
/ 2/ pi\\
6*|-1 + tan |3*x + --|| acot(x)
\ \ 4 // 4 *log(4)
----------------------- - ---------------
2/ pi\ 2
1 + tan |3*x + --| 1 + x
\ 4 /
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{6 \left(\tan^{2}{\left(3 x + \frac{\pi}{4} \right)} - 1\right)}{\tan^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1}$$
/ 2/ pi\\
6*|1 - cot |3*x + --|| acot(x)
\ \ 4 // 4 *log(4)
---------------------- - ---------------
2/ pi\ 2
1 + cot |3*x + --| 1 + x
\ 4 /
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{6 \cdot \left(- \cot^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1\right)}{\cot^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1}$$
acot(x)
// 0 for 6*x mod pi = 0\ 4 *log(4)
6*|< | - ---------------
\\sin(6*x) otherwise / 2
1 + x
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\sin{\left(6 x \right)} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\ acot(x) || | 4 *log(4) 6*|< 1 | - --------------- ||-------- otherwise | 2 \\csc(6*x) / 1 + x
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{1}{\csc{\left(6 x \right)}} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
acot(x) 2
4 *log(4) 24*sin (3*x)
- --------------- + --------------------------
2 / 4 \
1 + x | 4*sin (3*x)|
|1 + -----------|*sin(6*x)
| 2 |
\ sin (6*x) /
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{24 \sin^{2}{\left(3 x \right)}}{\left(\frac{4 \sin^{4}{\left(3 x \right)}}{\sin^{2}{\left(6 x \right)}} + 1\right) \sin{\left(6 x \right)}}$$
// 0 for 6*x mod pi = 0\ acot(x) || | 4 *log(4) 6*|< / pi\ | - --------------- ||cos|6*x - --| otherwise | 2 \\ \ 2 / / 1 + x
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\cos{\left(6 x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\ || | acot(x) || 1 | 4 *log(4) 6*|<------------- otherwise | - --------------- || / pi\ | 2 ||sec|6*x - --| | 1 + x \\ \ 2 / /
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{1}{\sec{\left(6 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// / 3*pi\ \ acot(x) || 1 for |6*x + ----| mod 2*pi = 0| 4 *log(4) 6*|< \ 2 / | - --------------- || | 2 \\sin(6*x) otherwise / 1 + x
$$\left(6 \left(\begin{cases} 1 & \text{for}\: \left(6 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(6 x \right)} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
/ pi\
acot(x) 12*cos|3*x - --|
4 *log(4) \ 2 /
- --------------- + -----------------------------
2 / 2/ pi\\
1 + x | cos |3*x - --||
| \ 2 /|
|1 + --------------|*cos(3*x)
| 2 |
\ cos (3*x) /
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{12 \cos{\left(3 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(3 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(3 x \right)}}\right) \cos{\left(3 x \right)}}$$
acot(x)
4 *log(4) 12*sec(3*x)
- --------------- + ----------------------------------
2 / 2 \
1 + x | sec (3*x) | / pi\
|1 + --------------|*sec|3*x - --|
| 2/ pi\| \ 2 /
| sec |3*x - --||
\ \ 2 //
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{12 \sec{\left(3 x \right)}}{\left(\frac{\sec^{2}{\left(3 x \right)}}{\sec^{2}{\left(3 x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(3 x - \frac{\pi}{2} \right)}}$$
// 0 for 6*x mod pi = 0\ || | acot(x) || 2*tan(3*x) | 4 *log(4) 6*|<------------- otherwise | - --------------- || 2 | 2 ||1 + tan (3*x) | 1 + x \\ /
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{2 \tan{\left(3 x \right)}}{\tan^{2}{\left(3 x \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\ || | acot(x) || 2*cot(3*x) | 4 *log(4) 6*|<------------- otherwise | - --------------- || 2 | 2 ||1 + cot (3*x) | 1 + x \\ /
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{2 \cot{\left(3 x \right)}}{\cot^{2}{\left(3 x \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
/pi \
acot(x) 12*csc|-- - 3*x|
4 *log(4) \2 /
- --------------- + -----------------------------
2 / 2/pi \\
1 + x | csc |-- - 3*x||
| \2 /|
|1 + --------------|*csc(3*x)
| 2 |
\ csc (3*x) /
$$- \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1} + \frac{12 \csc{\left(- 3 x + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- 3 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(3 x \right)}}\right) \csc{\left(3 x \right)}}$$
// 0 for 6*x mod pi = 0\
|| |
|| 2 | acot(x)
||------------------------ otherwise | 4 *log(4)
6*|
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(3 x \right)}}\right) \tan{\left(3 x \right)}} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\ acot(x)
|| | 4 *log(4)
6*|
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\sin{\left(6 x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// / 3*pi\ \ || 1 for |6*x + ----| mod 2*pi = 0| || \ 2 / | || | acot(x) || 2/ pi\ | 4 *log(4) 6*|<-1 + tan |3*x + --| | - --------------- || \ 4 / | 2 ||------------------- otherwise | 1 + x || 2/ pi\ | || 1 + tan |3*x + --| | \\ \ 4 / /
$$\left(6 \left(\begin{cases} 1 & \text{for}\: \left(6 x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(3 x + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(3 x + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\
|| |
|| sin(6*x) | acot(x)
||--------------------------- otherwise | 4 *log(4)
6*|
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{\sin{\left(6 x \right)}}{\left(1 + \frac{\sin^{2}{\left(6 x \right)}}{4 \sin^{4}{\left(3 x \right)}}\right) \sin^{2}{\left(3 x \right)}} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\ || | ||/ 0 for 6*x mod pi = 0 | acot(x) ||| | 4 *log(4) 6*|<| 2*cot(3*x) | - --------------- ||<------------- otherwise otherwise | 2 ||| 2 | 1 + x |||1 + cot (3*x) | \\\ /
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{2 \cot{\left(3 x \right)}}{\cot^{2}{\left(3 x \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\
|| |
|| / pi\ |
|| 2*sec|3*x - --| |
|| \ 2 / | acot(x)
||----------------------------- otherwise | 4 *log(4)
6*|
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{2 \sec{\left(3 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(3 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(3 x \right)}}\right) \sec{\left(3 x \right)}} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\ || | || 2*cos(3*x) | ||---------------------------------- otherwise | acot(x) ||/ 2 \ | 4 *log(4) 6*|<| cos (3*x) | / pi\ | - --------------- |||1 + --------------|*cos|3*x - --| | 2 ||| 2/ pi\| \ 2 / | 1 + x ||| cos |3*x - --|| | ||\ \ 2 // | \\ /
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{2 \cos{\left(3 x \right)}}{\left(\frac{\cos^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(3 x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
// 0 for 6*x mod pi = 0\ || | || 2*csc(3*x) | ||---------------------------------- otherwise | acot(x) ||/ 2 \ | 4 *log(4) 6*|<| csc (3*x) | /pi \ | - --------------- |||1 + --------------|*csc|-- - 3*x| | 2 ||| 2/pi \| \2 / | 1 + x ||| csc |-- - 3*x|| | ||\ \2 // | \\ /
$$\left(6 \left(\begin{cases} 0 & \text{for}\: 6 x \bmod \pi = 0 \\\frac{2 \csc{\left(3 x \right)}}{\left(\frac{\csc^{2}{\left(3 x \right)}}{\csc^{2}{\left(- 3 x + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- 3 x + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) - \frac{4^{\operatorname{acot}{\left(x \right)}} \log{\left(4 \right)}}{x^{2} + 1}$$
6*Piecewise((0, Mod(6*x = pi, 0)), (2*csc(3*x)/((1 + csc(3*x)^2/csc(pi/2 - 3*x)^2)*csc(pi/2 - 3*x)), True)) - 4^acot(x)*log(4)/(1 + x^2)