Question

Integrate x^4 * sqrt(1+x^2) dx

Answer 1

I'll give a medal if it was solved

Answer 2

Here is the solution but you may be disappointed it's not a beauty:
\[\int x^4 \sqrt{1+x^2} dx = 1/48 (x \sqrt{x^2+1} (8 x^4+2 x^2-3)+3 \sinh^{-1}(x))+C\]
To get this, start with substitution \[u=\tan x\]which will the lead you through several pages of calculations with trig integrals.

Answer 3

sorry i meant to say substitution \[x=\tan u\]