How Can You Solve This Challenging Integral Evaluation Problem?

[hadi amiri 4]

Evaluate
$$\int\frac{arctan(x)dx}{(1+x^2)^\frac{3}{2}}$$

 

[arildno]

Make the substitution:
$$x=\tan(u),\to\frac{dx}{du}=\frac{1}{\cos^{2}u}$$
Thus, we get:
$$dx=\frac{du}{\cos^{2}(u)}$$
and insertion in your integral yields:
$$\int\frac{arctan(x)}{(1+x^{2})^{\frac{3}{2}}}=\int{u}\cos(u)du$$

 

[hadi amiri 4]

your solution seems nice
honestly i thought it is a hard one,becouse i picked it form "A coures of pure mathematics"