# Thread: Using u-substitution, integrate ∫(x^3)(x^2-1)^(3/2)dx

1. ## Using u-substitution, integrate ∫(x^3)(x^2-1)^(3/2)dx

∫(x^3)(x^2-1)^(3/2)dx

I tried u=x^2 - 1, but then I get (1/2)du=xdx, and I have an x^3, so that's not working...what should I do?

2. On the contrary, $u = x^2 - 1$ is an ideal substitution.

$du = 2x~dx$ yields

$\int (x^2)(x^2-1)^{\frac{3}{2}}~du = \int (u+1)u^{\frac{3}{2}}~du$

Do you see why?

3. It's x^3 though, not x^2

4. $\frac{x^3}{2x} = \frac{1}{2}x^2$

I forgot to put the constant in my previous post.