/ 1 x*cos(x)\
2*|------ - --------|*sin(x)
/ 2\ |sin(x) 2 |
2*x 2*x*atan\x / \ sin (x) /
----------------- + ------------ + ----------------------------
/ 4\ / 2\ 2 x
\1 + x /*\1 - x / / 2\
\1 - x /
$$\frac{2 x}{\left(1 - x^{2}\right) \left(x^{4} + 1\right)} + \frac{2 x \operatorname{atan}{\left(x^{2} \right)}}{\left(1 - x^{2}\right)^{2}} + \frac{2 \left(- \frac{x \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right) \sin{\left(x \right)}}{x}$$
/ 2 \
| 2*cos(x) 2*x*cos (x) |
|x - -------- + ----------- x*cos(x) / x*cos(x)\ |
| sin(x) 2 -1 + -------- / 2\ 2 / 2\ 2 4 |-1 + --------|*cos(x)|
| sin (x) sin(x) atan\x / 1 4*x *atan\x / 4*x 4*x \ sin(x) / |
2*|-------------------------- + ------------- + ---------- - ------------------ - ------------- + ------------------- + ------------------- - ----------------------|
| x 2 2 / 4\ / 2\ 3 2 2 x*sin(x) |
| x / 2\ \1 + x /*\-1 + x / / 2\ / 4\ / 2\ / 4\ / 2\ |
\ \-1 + x / \-1 + x / \1 + x /*\-1 + x / \1 + x / *\-1 + x / /
$$2 \left(\frac{4 x^{4}}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)^{2}} + \frac{4 x^{2}}{\left(x^{2} - 1\right)^{2} \left(x^{4} + 1\right)} - \frac{4 x^{2} \operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{3}} - \frac{1}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}}{x} + \frac{\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1}{x^{2}}\right)$$
/ 2 3 / 2 \ / 2 \ \
| 6*cos (x) 5*x*cos(x) 6*x*cos (x) | 2*cos(x) 2*x*cos (x)| | 2*cos(x) 2*x*cos (x)| |
| x*cos(x) -3 - --------- + ---------- + ----------- / x*cos(x)\ 2*|x - -------- + -----------| 2*|x - -------- + -----------|*cos(x) / x*cos(x)\ |
|-1 + -------- 2 sin(x) 3 2*|-1 + --------| | sin(x) 2 | 7 3 5 / 2\ 3 3 / 2\ | sin(x) 2 | 2*|-1 + --------|*cos(x)|
| sin(x) sin (x) sin (x) \ sin(x) / \ sin (x) / 32*x 24*x 24*x 12*x*atan\x / 12*x 20*x 24*x *atan\x / \ sin (x) / \ sin(x) / |
2*|------------- - ----------------------------------------- - ----------------- - ------------------------------ - ------------------- - ------------------- - -------------------- - ------------- + ------------------- + ------------------- + -------------- + ------------------------------------- + ------------------------|
| x x 3 2 3 3 2 2 3 2 2 4 x*sin(x) 2 |
| x x / 4\ / 2\ / 4\ / 2\ / 4\ / 2\ / 2\ / 4\ / 2\ / 4\ / 2\ / 2\ x *sin(x) |
\ \1 + x / *\-1 + x / \1 + x /*\-1 + x / \1 + x / *\-1 + x / \-1 + x / \1 + x /*\-1 + x / \1 + x / *\-1 + x / \-1 + x / /
$$2 \left(- \frac{32 x^{7}}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)^{3}} - \frac{24 x^{5}}{\left(x^{2} - 1\right)^{2} \left(x^{4} + 1\right)^{2}} + \frac{20 x^{3}}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)^{2}} - \frac{24 x^{3}}{\left(x^{2} - 1\right)^{3} \left(x^{4} + 1\right)} + \frac{24 x^{3} \operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{4}} + \frac{12 x}{\left(x^{2} - 1\right)^{2} \left(x^{4} + 1\right)} - \frac{12 x \operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{3}} + \frac{\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1}{x} + \frac{2 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{\frac{5 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{6 x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 3 - \frac{6 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}}{x} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x^{2}} - \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right)}{x^{3}}\right)$$