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(-5*sin(x)*sin(cos(x))-5*cos(x)*cos(cos(x))*sin(x))/(x+3)-5*cos(x)*sin(cos(x))/(x+3)^2
Общий знаменатель (-5*sin(x)*sin(cos(x))-5*cos(x)*cos(cos(x))*sin(x))/(x+3)-5*cos(x)*sin(cos(x))/(x+3)^2
Решение
Вы ввели
[src]
-5*sin(x)*sin(cos(x)) - 5*cos(x)*cos(cos(x))*sin(x) 5*cos(x)*sin(cos(x))
--------------------------------------------------- - --------------------
x + 3 2
(x + 3)
$$- \frac{5 \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{\left(x + 3\right)^{2}} + \frac{- 5 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 5 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}}{x + 3}$$
(-5*sin(x)*sin(cos(x)) - 5*cos(x)*cos(cos(x))*sin(x))/(x + 3) - 5*cos(x)*sin(cos(x))/((x + 3)^2)
Общее упрощение
[src]
5*(-cos(x)*sin(cos(x)) + (-3 - x)*(cos(x)*cos(cos(x)) + sin(cos(x)))*sin(x))
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2
(3 + x)
$$\frac{5 \left(\left(- x - 3\right) \left(\cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} + \sin{\left(\cos{\left(x \right)} \right)}\right) \sin{\left(x \right)} - \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right)}{\left(x + 3\right)^{2}}$$
5*(-cos(x)*sin(cos(x)) + (-3 - x)*(cos(x)*cos(cos(x)) + sin(cos(x)))*sin(x))/(3 + x)^2
Рациональный знаменатель
[src]
5*sin(x)*sin(cos(x)) 5*cos(x)*sin(cos(x)) 5*cos(x)*cos(cos(x))*sin(x)
- -------------------- - -------------------- - ---------------------------
3 + x 2 3 + x
(3 + x)
$$- \frac{5 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)}}{x + 3} - \frac{5 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}}{x + 3} - \frac{5 \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{\left(x + 3\right)^{2}}$$
2
(3 + x) *(-5*sin(x)*sin(cos(x)) - 5*cos(x)*cos(cos(x))*sin(x)) - 5*(3 + x)*cos(x)*sin(cos(x))
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3
(3 + x)
$$\frac{\left(x + 3\right)^{2} \left(- 5 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 5 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}\right) - 5 \left(x + 3\right) \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{\left(x + 3\right)^{3}}$$
((3 + x)^2*(-5*sin(x)*sin(cos(x)) - 5*cos(x)*cos(cos(x))*sin(x)) - 5*(3 + x)*cos(x)*sin(cos(x)))/(3 + x)^3
Объединение рациональных выражений
[src]
5*(-cos(x)*sin(cos(x)) + (3 + x)*(-sin(cos(x)) - cos(x)*cos(cos(x)))*sin(x))
----------------------------------------------------------------------------
2
(3 + x)
$$\frac{5 \left(\left(x + 3\right) \left(- \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - \sin{\left(\cos{\left(x \right)} \right)}\right) \sin{\left(x \right)} - \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right)}{\left(x + 3\right)^{2}}$$
5*(-cos(x)*sin(cos(x)) + (3 + x)*(-sin(cos(x)) - cos(x)*cos(cos(x)))*sin(x))/(3 + x)^2
Комбинаторика
[src]
-5*(cos(x)*sin(cos(x)) + 3*sin(x)*sin(cos(x)) + x*sin(x)*sin(cos(x)) + 3*cos(x)*cos(cos(x))*sin(x) + x*cos(x)*cos(cos(x))*sin(x))
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2
(3 + x)
$$- \frac{5 \left(x \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} + x \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)} + 3 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} + 3 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)} + \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}\right)}{\left(x + 3\right)^{2}}$$
-5*(cos(x)*sin(cos(x)) + 3*sin(x)*sin(cos(x)) + x*sin(x)*sin(cos(x)) + 3*cos(x)*cos(cos(x))*sin(x) + x*cos(x)*cos(cos(x))*sin(x))/(3 + x)^2
Собрать выражение
[src]
-5*sin(x)*sin(cos(x)) - 5*cos(x)*cos(cos(x))*sin(x) 5*cos(x)*sin(cos(x))
--------------------------------------------------- - --------------------
3 + x 2
(3 + x)
$$\frac{- 5 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 5 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}}{x + 3} - \frac{5 \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{\left(x + 3\right)^{2}}$$
5*cos(x - cos(x)) 5*sin(-cos(x) + 2*x) 5*sin(2*x + cos(x)) 5*sin(x + cos(x)) 5*cos(x + cos(x)) 5*sin(x - cos(x))
- ----------------- - -------------------- - ------------------- - ----------------- + ----------------- + -----------------
6 + 2*x 12 + 4*x 12 + 4*x 2 6 + 2*x 2
18 + 2*x + 12*x 18 + 2*x + 12*x
$$\frac{5 \sin{\left(x - \cos{\left(x \right)} \right)}}{2 x^{2} + 12 x + 18} - \frac{5 \sin{\left(x + \cos{\left(x \right)} \right)}}{2 x^{2} + 12 x + 18} - \frac{5 \sin{\left(2 x - \cos{\left(x \right)} \right)}}{4 x + 12} - \frac{5 \sin{\left(2 x + \cos{\left(x \right)} \right)}}{4 x + 12} - \frac{5 \cos{\left(x - \cos{\left(x \right)} \right)}}{2 x + 6} + \frac{5 \cos{\left(x + \cos{\left(x \right)} \right)}}{2 x + 6}$$
-5*cos(x - cos(x))/(6 + 2*x) - 5*sin(-cos(x) + 2*x)/(12 + 4*x) - 5*sin(2*x + cos(x))/(12 + 4*x) - 5*sin(x + cos(x))/(18 + 2*x^2 + 12*x) + 5*cos(x + cos(x))/(6 + 2*x) + 5*sin(x - cos(x))/(18 + 2*x^2 + 12*x)
Общий знаменатель
[src]
-15*sin(x)*sin(cos(x)) - 5*cos(x)*sin(cos(x)) - 15*cos(x)*cos(cos(x))*sin(x) - 5*x*sin(x)*sin(cos(x)) - 5*x*cos(x)*cos(cos(x))*sin(x)
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2
9 + x + 6*x
$$\frac{- 5 x \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 5 x \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)} - 15 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 15 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)} - 5 \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{x^{2} + 6 x + 9}$$
(-15*sin(x)*sin(cos(x)) - 5*cos(x)*sin(cos(x)) - 15*cos(x)*cos(cos(x))*sin(x) - 5*x*sin(x)*sin(cos(x)) - 5*x*cos(x)*cos(cos(x))*sin(x))/(9 + x^2 + 6*x)
Численный ответ
[src]
(-5.0*sin(x)*sin(cos(x)) - 5.0*cos(x)*cos(cos(x))*sin(x))/(3.0 + x) - 0.555555555555556*cos(x)*sin(cos(x))/(1 + 0.333333333333333*x)^2
(-5.0*sin(x)*sin(cos(x)) - 5.0*cos(x)*cos(cos(x))*sin(x))/(3.0 + x) - 0.555555555555556*cos(x)*sin(cos(x))/(1 + 0.333333333333333*x)^2
Степени
[src]
-5*sin(x)*sin(cos(x)) - 5*cos(x)*cos(cos(x))*sin(x) 5*cos(x)*sin(cos(x))
--------------------------------------------------- - --------------------
3 + x 2
(3 + x)
$$\frac{- 5 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 5 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}}{x + 3} - \frac{5 \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{\left(x + 3\right)^{2}}$$
-5*sin(x)*sin(cos(x)) - 5*cos(x)*cos(cos(x))*sin(x) 5*cos(x)*sin(cos(x))
--------------------------------------------------- - --------------------
x + 3 2
(x + 3)
$$\frac{- 5 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 5 \sin{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)}}{x + 3} - \frac{5 \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)}}{\left(x + 3\right)^{2}}$$
/ / I*x -I*x\ / I*x -I*x\\
| |e e | | e e ||
/ / I*x -I*x\ / I*x -I*x\\ | I*|---- + -----| I*|- ---- - -----||
| | e e | |e e || / I*x -I*x\ | \ 2 2 / \ 2 2 /| / / I*x -I*x\ / I*x -I*x\\
| I*|- ---- - -----| I*|---- + -----|| |e e | |e e | / -I*x I*x\ | | e e | |e e ||
| \ 2 2 / \ 2 2 /| / -I*x I*x\ 5*I*|---- + -----|*|----------------- + -------------------|*\- e + e / / I*x -I*x\ | I*|- ---- - -----| I*|---- + -----||
5*\- e + e /*\- e + e / \ 2 2 / \ 2 2 / |e e | | \ 2 2 / \ 2 2 /|
-------------------------------------------------------------- + ----------------------------------------------------------------------------- 5*I*|---- + -----|*\- e + e /
4 2 \ 2 2 /
---------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------
3 + x 2
2*(3 + x)
$$\frac{\frac{5 i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{i x} - e^{- i x}\right) \left(\frac{e^{i \left(- \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}\right)}}{2} + \frac{e^{i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}}{2}\right)}{2} + \frac{5 \left(e^{i x} - e^{- i x}\right) \left(- e^{i \left(- \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}\right)} + e^{i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}\right)}{4}}{x + 3} + \frac{5 i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(- e^{i \left(- \frac{e^{i x}}{2} - \frac{e^{- i x}}{2}\right)} + e^{i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}\right)}{2 \left(x + 3\right)^{2}}$$
(5*(-exp(i*(-exp(i*x)/2 - exp(-i*x)/2)) + exp(i*(exp(i*x)/2 + exp(-i*x)/2)))*(-exp(-i*x) + exp(i*x))/4 + 5*i*(exp(i*x)/2 + exp(-i*x)/2)*(exp(i*(exp(i*x)/2 + exp(-i*x)/2))/2 + exp(i*(-exp(i*x)/2 - exp(-i*x)/2))/2)*(-exp(-i*x) + exp(i*x))/2)/(3 + x) + 5*i*(exp(i*x)/2 + exp(-i*x)/2)*(-exp(i*(-exp(i*x)/2 - exp(-i*x)/2)) + exp(i*(exp(i*x)/2 + exp(-i*x)/2)))/(2*(3 + x)^2)