________ / 2 \
/ 2 | 1 x |
t*\/ x + 1 *|----------- - -----------|
| ________ 3/2|
| / 2 / 2 \ |
1 atan(x) \\/ x + 1 \x + 1/ /
---------- - ------- - -----------------------------------------
/ 2\ 2 x
x*\1 + x / x
$$- \frac{t \sqrt{x^{2} + 1} \left(- \frac{x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} + 1}}\right)}{x} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2}} + \frac{1}{x \left(x^{2} + 1\right)}$$
/ 2 \ / 2 \ / 2 \
| x | | x | | x |
t*|-1 + ------| t*|-1 + ------| 3*t*|1 - ------|
| 2| | 2| | 2|
2 2 2*atan(x) \ 1 + x / \ 1 + x / \ 1 + x /
- --------- - ----------- + --------- + --------------- - --------------- + ----------------
2 2 / 2\ 3 2 2 2
/ 2\ x *\1 + x / x 1 + x x 1 + x
\1 + x /
$$\frac{3 t \left(- \frac{x^{2}}{x^{2} + 1} + 1\right)}{x^{2} + 1} + \frac{t \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{t \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2}} - \frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{2 \operatorname{atan}{\left(x \right)}}{x^{3}} - \frac{2}{x^{2} \left(x^{2} + 1\right)}$$
/ 2 4 \
/ 2 \ / 2 \ / 2 \ / 2 \ | 6*x 5*x | / 2 \
| x | | x | | x | | x | 3*t*|1 - ------ + ---------| | x |
2*t*|-1 + ------| t*x*|-1 + ------| t*|-1 + ------| 6*t*|1 - ------| | 2 2| 6*t*x*|1 - ------|
| 2| | 2| | 2| | 2| | 1 + x / 2\ | | 2|
6*atan(x) 4 6 8*x \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ \1 + x / / \ 1 + x /
- --------- + ----------- + ----------- + --------- + ----------------- - ----------------- - --------------- - ---------------- + ---------------------------- + ------------------
4 2 3 / 2\ 3 3 2 / 2\ / 2\ / 2\ 2
x / 2\ x *\1 + x / / 2\ x / 2\ x*\1 + x / x*\1 + x / x*\1 + x / / 2\
x*\1 + x / \1 + x / \1 + x / \1 + x /
$$\frac{6 t x \left(- \frac{x^{2}}{x^{2} + 1} + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{t x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{6 t \left(- \frac{x^{2}}{x^{2} + 1} + 1\right)}{x \left(x^{2} + 1\right)} - \frac{t \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x \left(x^{2} + 1\right)} + \frac{3 t \left(\frac{5 x^{4}}{\left(x^{2} + 1\right)^{2}} - \frac{6 x^{2}}{x^{2} + 1} + 1\right)}{x \left(x^{2} + 1\right)} + \frac{2 t \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{3}} + \frac{8 x}{\left(x^{2} + 1\right)^{3}} + \frac{4}{x \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{4}} + \frac{6}{x^{3} \left(x^{2} + 1\right)}$$