Ideas as to how I should start to integrate this one?

[LocationX]

\int (C^2x^2-x^4)^{0.5} dx

C is a constant

any ideas as to how I shoud start to integrate this one?

 

[LeonhardEuler]

Yeah, just factor out x^2, so you have
\int x\sqrt{C^2-x^2}dx
Then just make the substitution u=x^2.

 

[LocationX]

so then how would I integrate

\int (C^2-u)^{0.5}

 

[Luminous Blob]

You can make another substitution, e.g. z = C^2 - u or just make your original substitution u = C^2 - x^2, which gives

du = -2x dx

\frac{du}{-2x} = dx

then you just use your normal integration rules.

 

[arildno]

Yeah, just factor out x^2, so you have
\int x\sqrt{C^2-x^2}dx
Then just make the substitution u=x^2.

Just a minor correction.
We should have:
\int\sqrt{C^{2}x^{2}-x^{4}}dx=\int|x|\sqrt{C^{2}-x^{2}}dx