# Calculational Integral

1. Oct 7, 2007

### azatkgz

1. The problem statement, all variables and given/known data

$$\int\frac{x^3dx}{\sqrt{2-x}}$$

3. The attempt at a solution
I solved it in this way
for v=2-x
$$\int-\frac{(2-v)^3dv}{\sqrt{v}}=-\int\frac{(8-12v+6v^2+v^3)dv}{\sqrt{v}} =-\int\frac{8dv}{\sqrt{v}}+\int 12\sqrt{v}dv-\int 6v\sqrt{v}dv-\int v^2\sqrt{v}dv$$
is it true?
Is there any other methods?

Last edited: Oct 7, 2007
2. Oct 7, 2007

### neutrino

That's one way of doing it. If you substitute v2 for 2-x, you will have a radical-free expression to integrate.

3. Oct 7, 2007

### azatkgz

Ok,very nice.