Question

How to integrate
\[\int_{ - a}^a {\frac{{{x^2}}}
{{\sqrt {{x^2} + {a^2}} }}dx} \]

Answer 1

I have try set \[x = a\tan \theta \]
but at last I have to integrate\[{a^2}\int {{{\tan }^2}\theta \sec \theta d\theta } \]
which is still something I can't integrate out...

Answer 2

hmm you are just making it complicated.. try to make it more simple ^.^

Answer 3

Use the method of Integration by parts?

Answer 4

i don't think so... but mybe it can be..

Answer 5

Desperate...Take your time guys...