How do I integrate a rational function with a square root in the denominator?

[thomas49th]

$$\int \frac{x}{\sqrt(1-4x^{2})}dx$$
If it was just a constant on top I could turn it into an arcsin, but there is a stupid x there, so not to sure. I though about intergrating by parts, but their must be an easier method than that?

Thanks

 

[quasar987]

Well, you could make the x above "disappear" by doing a change of variable u=4x².

 

[Dick]

Try the substitution u=1-4x^2.

 

[thomas49th]

cheers thanks got it!

btw, how do you spot a substitution? There is a rule(s) for it. When somthingis the product or differential of somthing else?

Thanks :)

 

[Dick]

When you see a multiple of the derivative of something else in the numerator, it's a dead giveaway for a substitution.