Try and intergrate this

  • Thread starter thomas49th
  • Start date
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.
  • #1
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[tex]\int \frac{x}{\sqrt(1-4x^{2})}dx[/tex]
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
 
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  • #2
Well, you could make the x above "disappear" by doing a change of variable u=4x².
 
  • #3
Try the substitution u=1-4x^2.
 
  • #4
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 :)
 
  • #5
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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