Find the following indefinite integral including a root and fraction

Question

I'm trying to solve the following indefinite integral. I know I need to do substitution, but I simply don't know how to do it.

$$\int \:\frac{x^2}{\sqrt{\left(x^2+1\right)^3}}$$

Answer 1

Hint: try substitution $x=\tan t$. You'll get $$\int\frac{\tan^2 t}{(1/\cos^2 t)^{3/2}}\frac{dt}{\cos^2 t}=\int \frac{\sin^2 t}{\cos t} dt,$$ which is almost from the table.