/ sin(x) \
|e ___ sin(x)|
-|------- + \/ x *cos(x)*e |
| ___ |
\2*\/ x /
----------------------------------
_________________
/ 2*sin(x)
\/ 1 - x*e
$$- \frac{\sqrt{x} e^{\sin{\left(x \right)}} \cos{\left(x \right)} + \frac{e^{\sin{\left(x \right)}}}{2 \sqrt{x}}}{\sqrt{- x e^{2 \sin{\left(x \right)}} + 1}}$$
/ / 1 ___ \ 2*sin(x)\
| (1 + 2*x*cos(x))*|----- + 2*\/ x *cos(x)|*e |
| | ___ | |
| 1 ___ ___ 2 cos(x) \\/ x / | sin(x)
|------ + \/ x *sin(x) - \/ x *cos (x) - ------ - ---------------------------------------------------|*e
| 3/2 ___ / 2*sin(x)\ |
\4*x \/ x 4*\1 - x*e / /
--------------------------------------------------------------------------------------------------------------
_________________
/ 2*sin(x)
\/ 1 - x*e
$$\frac{\left(\sqrt{x} \sin{\left(x \right)} - \sqrt{x} \cos^{2}{\left(x \right)} - \frac{\left(2 \sqrt{x} \cos{\left(x \right)} + \frac{1}{\sqrt{x}}\right) \left(2 x \cos{\left(x \right)} + 1\right) e^{2 \sin{\left(x \right)}}}{4 \left(- x e^{2 \sin{\left(x \right)}} + 1\right)} - \frac{\cos{\left(x \right)}}{\sqrt{x}} + \frac{1}{4 x^{\frac{3}{2}}}\right) e^{\sin{\left(x \right)}}}{\sqrt{- x e^{2 \sin{\left(x \right)}} + 1}}$$
/ 2 / 1 ___ \ 4*sin(x) / 1 ___ \ / 2 \ 2*sin(x) / 1 ___ 2 4*cos(x) ___ \ 2*sin(x)\
| 3*(1 + 2*x*cos(x)) *|----- + 2*\/ x *cos(x)|*e |----- + 2*\/ x *cos(x)|*\2*cos(x) - x*sin(x) + 2*x*cos (x)/*e (1 + 2*x*cos(x))*|---- - 4*\/ x *cos (x) - -------- + 4*\/ x *sin(x)|*e |
| 2 | ___ | | ___ | | 3/2 ___ | |
| 3 ___ ___ 3 3*cos (x) 3*sin(x) 3*cos(x) ___ \\/ x / \\/ x / \x \/ x / | sin(x)
|- ------ + \/ x *cos(x) - \/ x *cos (x) - --------- + -------- + -------- + 3*\/ x *cos(x)*sin(x) - ------------------------------------------------------ - ---------------------------------------------------------------------- + -------------------------------------------------------------------------------|*e
| 5/2 ___ ___ 3/2 2 / 2*sin(x)\ / 2*sin(x)\ |
| 8*x 2*\/ x 2*\/ x 4*x / 2*sin(x)\ 2*\1 - x*e / 4*\1 - x*e / |
\ 8*\1 - x*e / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_________________
/ 2*sin(x)
\/ 1 - x*e
$$\frac{\left(3 \sqrt{x} \sin{\left(x \right)} \cos{\left(x \right)} - \sqrt{x} \cos^{3}{\left(x \right)} + \sqrt{x} \cos{\left(x \right)} - \frac{\left(2 \sqrt{x} \cos{\left(x \right)} + \frac{1}{\sqrt{x}}\right) \left(- x \sin{\left(x \right)} + 2 x \cos^{2}{\left(x \right)} + 2 \cos{\left(x \right)}\right) e^{2 \sin{\left(x \right)}}}{2 \left(- x e^{2 \sin{\left(x \right)}} + 1\right)} - \frac{3 \left(2 \sqrt{x} \cos{\left(x \right)} + \frac{1}{\sqrt{x}}\right) \left(2 x \cos{\left(x \right)} + 1\right)^{2} e^{4 \sin{\left(x \right)}}}{8 \left(- x e^{2 \sin{\left(x \right)}} + 1\right)^{2}} + \frac{\left(2 x \cos{\left(x \right)} + 1\right) \left(4 \sqrt{x} \sin{\left(x \right)} - 4 \sqrt{x} \cos^{2}{\left(x \right)} - \frac{4 \cos{\left(x \right)}}{\sqrt{x}} + \frac{1}{x^{\frac{3}{2}}}\right) e^{2 \sin{\left(x \right)}}}{4 \left(- x e^{2 \sin{\left(x \right)}} + 1\right)} + \frac{3 \sin{\left(x \right)}}{2 \sqrt{x}} - \frac{3 \cos^{2}{\left(x \right)}}{2 \sqrt{x}} + \frac{3 \cos{\left(x \right)}}{4 x^{\frac{3}{2}}} - \frac{3}{8 x^{\frac{5}{2}}}\right) e^{\sin{\left(x \right)}}}{\sqrt{- x e^{2 \sin{\left(x \right)}} + 1}}$$