2
2 2 atan (x)
atan (x) 2*x *atan(x)*e
2*x*e + ----------------------
2
1 + x
$$\frac{2 x^{2} e^{\operatorname{atan}^{2}{\left(x \right)}} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + 2 x e^{\operatorname{atan}^{2}{\left(x \right)}}$$
/ 2 3 2 2 \ 2
| x 2*x *atan(x) 2*x *atan (x) 4*x*atan(x)| atan (x)
2*|1 + --------- - ------------ + ------------- + -----------|*e
| 2 2 2 2 |
| / 2\ / 2\ / 2\ 1 + x |
\ \1 + x / \1 + x / \1 + x / /
$$2 \left(- \frac{2 x^{3} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{4 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + 1\right) e^{\operatorname{atan}^{2}{\left(x \right)}}$$
/ 3 2 3 2 2 3 2 4 2 \ 2
| 3*x 3*x 7*x *atan(x) 6*x *atan (x) 2*x *atan (x) 3*x *atan(x) 4*x *atan(x) 6*x*atan (x)| atan (x)
4*|3*atan(x) - --------- + ------ - ------------ - ------------- + ------------- + ------------ + ------------ + ------------|*e
| 2 2 2 2 2 2 2 2 |
| / 2\ 1 + x 1 + x / 2\ / 2\ / 2\ / 2\ 1 + x |
\ \1 + x / \1 + x / \1 + x / \1 + x / \1 + x / /
----------------------------------------------------------------------------------------------------------------------------------------
2
1 + x
$$\frac{4 \left(\frac{4 x^{4} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 x^{3} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 x^{3}}{\left(x^{2} + 1\right)^{2}} - \frac{7 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{2 x^{2} \operatorname{atan}^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 x^{2} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6 x \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + 3 \operatorname{atan}{\left(x \right)}\right) e^{\operatorname{atan}^{2}{\left(x \right)}}}{x^{2} + 1}$$