Integration problem

crm08

1. The problem statement, all variables and given/known data

[tex]\int(\frac{x}{\sqrt{1-x^{2}}})dx[/tex]

2. Relevant equations



3. The attempt at a solution

My calculator tells me that the answer should be -sqrt(1-x^2) but if I pick u = sqrt(1-x^2), then dx = (sqrt(1-x^2)*du)/x, which leaves me with -integral((sqrt(1-x^2)/u)du), the problem I am having is getting rid of the "ln(u)" in my final answer, any suggestions?

rock.freak667

If u^2=1-x^2
2u du =-2x dx => - u du = x dx

Now you'd just get

[tex]\frac{-u}{u} du[/tex]

crm08

ok got it, thank you

Mark44

Another substitution that works is u = 1 - x^2, du = -2xdx.
The integrand then becomes -(1/2)du/u^(1/2), which is also an easy one to integrate.