integral: x/(sqrt[x^2+2x-3])

[thebenji]

Evaluate the indefinite integral:

x/(sqrt[x^2+2x-3])dx

I factor the denominator:

= x/sqrt[(x+3)(x-1)]dx

Let u=x+1, x=u-1, du=dx

= (u-1)/sqrt[(u+2)(u-2)]du

= (u-1)/sqrt(u^2-4)

Now what do I do?

 

[Steem]

Have you learned how to use trig substitution?

sqrt(u^2-4) = 2tan(theta) We'll just call theta 't'

u = 2sec(t)
du = 2sec(t)tan(t)d(t)
substitute these values in for u and du then integrate
If you get a clear understanding of trig substitution these problems will be much easier!