∫x^2/√(x^2 + 1) dx
How can I do this?
Trig. sub. will do it, but I'm afraid that your first sub. won't work.
Or make $\displaystyle \frac{{x^2 }}
{{\sqrt {x^2 + 1} }} = \sqrt {x^2 + 1} - \frac{1}
{{\sqrt {x^2 + 1} }}.$
You can tackle the first one via trig. - hyperbolic substitution or integration by parts, the another one is a classic one.