5 / 2/ ___\\ 4 / ___\
atan (3*x)*\1 + tan \\/ x // 15*atan (3*x)*tan\\/ x /
---------------------------- + ------------------------
___ 2
2*\/ x 1 + 9*x
$$\frac{15 \tan{\left(\sqrt{x} \right)} \operatorname{atan}^{4}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{5}{\left(3 x \right)}}{2 \sqrt{x}}$$
/ / / ___\\ \
| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
| atan (3*x)*\1 + tan \\/ x //*|- ---- + ------------| |
| / ___\ | 3/2 x | / 2/ ___\\ |
3 | 90*(-2 + 3*x*atan(3*x))*tan\\/ x / \ x / 15*\1 + tan \\/ x //*atan(3*x)|
atan (3*x)*|- ---------------------------------- + ---------------------------------------------------- + ------------------------------|
| 2 4 ___ / 2\ |
| / 2\ \/ x *\1 + 9*x / |
\ \1 + 9*x / /
$$\left(\frac{\left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}{4} - \frac{90 \left(3 x \operatorname{atan}{\left(3 x \right)} - 2\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} + \frac{15 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)}\right) \operatorname{atan}^{3}{\left(3 x \right)}$$
/ / 2 2 \ / / ___\ / 2/ ___\\ 2/ ___\\ / / ___\\ \
| | 2 6 36*x*atan(3*x) 36*x *atan (3*x)| / ___\ 3 / 2/ ___\\ | 3 6*tan\\/ x / 2*\1 + tan \\/ x // 4*tan \\/ x /| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
|270*|- atan (3*x) + -------- - -------------- + ----------------|*tan\\/ x / atan (3*x)*\1 + tan \\/ x //*|---- - ------------ + ------------------- + -------------| 45*atan (3*x)*\1 + tan \\/ x //*|- ---- + ------------| |
| | 2 2 2 | | 5/2 2 3/2 3/2 | | 3/2 x | / 2/ ___\\ |
2 | \ 1 + 9*x 1 + 9*x 1 + 9*x / \x x x x / \ x / 135*\1 + tan \\/ x //*(-2 + 3*x*atan(3*x))*atan(3*x)|
atan (3*x)*|---------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------- - ----------------------------------------------------|
| 2 8 / 2\ 2 |
| / 2\ 4*\1 + 9*x / ___ / 2\ |
\ \1 + 9*x / \/ x *\1 + 9*x / /
$$\left(\frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \left(- \frac{6 \tan{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{4 \tan^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) \operatorname{atan}^{3}{\left(3 x \right)}}{8} + \frac{45 \left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}{4 \left(9 x^{2} + 1\right)} + \frac{270 \left(\frac{36 x^{2} \operatorname{atan}^{2}{\left(3 x \right)}}{9 x^{2} + 1} - \frac{36 x \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1} - \operatorname{atan}^{2}{\left(3 x \right)} + \frac{6}{9 x^{2} + 1}\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} - \frac{135 \left(3 x \operatorname{atan}{\left(3 x \right)} - 2\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)^{2}}\right) \operatorname{atan}^{2}{\left(3 x \right)}$$