2 ___
atan (x) 2*\/ x *atan(x)
6*x + -------- + ---------------
___ 2
2*\/ x 1 + x
$$\frac{2 \sqrt{x} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + 6 x + \frac{\operatorname{atan}^{2}{\left(x \right)}}{2 \sqrt{x}}$$
___ 2 3/2
2*\/ x atan (x) 4*x *atan(x) 2*atan(x)
6 + --------- - -------- - -------------- + --------------
2 3/2 2 ___ / 2\
/ 2\ 4*x / 2\ \/ x *\1 + x /
\1 + x / \1 + x /
$$- \frac{4 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} + 6 + \frac{2 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{4 x^{\frac{3}{2}}}$$
3/2 2 ___ 5/2
12*x 3 3*atan (x) 10*\/ x *atan(x) 16*x *atan(x) 3*atan(x)
- --------- + --------------- + ---------- - ---------------- + --------------- - ---------------
3 2 5/2 2 3 3/2 / 2\
/ 2\ ___ / 2\ 8*x / 2\ / 2\ 2*x *\1 + x /
\1 + x / \/ x *\1 + x / \1 + x / \1 + x /
$$\frac{16 x^{\frac{5}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x^{\frac{3}{2}}}{\left(x^{2} + 1\right)^{3}} - \frac{10 \sqrt{x} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{3 \operatorname{atan}{\left(x \right)}}{2 x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{8 x^{\frac{5}{2}}}$$