# Try and intergrate this

• thomas49th
In summary, when integrating \frac{x}{\sqrt(1-4x^{2})}dx, a change of variable u=1-4x^2 can be used to simplify the integration process. It can be spotted by looking for a multiple of the derivative of something else in the numerator.

#### 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

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

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

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 :)

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

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