Calculating Integral: \int\frac{x^3dx}{\sqrt{2-x}} Solution and Alternatives

[azatkgz]

Homework Statement

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

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?

 

[neutrino]

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

 

[azatkgz]

Ok,very nice.