Evaluate the integral

Integral of (x^3)/(1+x^2)^(1/2).

I thought you would use x=tan of theta, but that doesn't seem to work, unless I messed up somewhere.

Question

Evaluate the integral

Integral of (x^3)/(1+x^2)^(1/2).

I thought you would use x=tan of theta, but that doesn't seem to work, unless I messed up somewhere.

anonymous · Answer

1/3 (x^2-2)sqrt(X^2+1)

anonymous · Answer

+C

anonymous · Answer

Ya, I know what the answer is. I just don't know how to get to it.

anonymous · Answer

you can use the u subsitution

anonymous · Answer

u=x^2+1
du=2x dx
du/2=dx

anonymous · Answer

or u=x^2
du=2x dx

1/2 integral u/sqrt(u+1)

anonymous · Answer

there are many ways to do this
you can also rewrite thequestion as
x^2*x/sqrt(x^2+1)

anonymous · Answer

Would using x=tan of theta work?

jamesj · Answer

It would, but it would just make the problem more complicated.  Why use a trig substitution when you can just use a polynominal substitution?

anonymous · Answer