integrating using u-substitution

[michi]

I can't seem to wrap my head around this function


integral [(x^3)/sqrt(x^2+1)] dx

The answer is 1/3 sqrt(x^2 +1) * (x^2-2) +C

I don't know how they got that answer. Help is greatly appreciated.

 

[tkhunny]

Try both of these and see which you like better:

u = x^2 + 1 ==> x^2 = u - 1

or

u^2 = x^2 + 1 ==> x^2 = u^2 - 1