Integrating: Solving the Problem of Ln(u) in Answer

[crm08]

Homework Statement

\int(\frac{x}{\sqrt{1-x^{2}}})dx

Homework Equations

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

\frac{-u}{u} du

 

[crm08]

ok got it, thank you

 

[Mark44]

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

Now you'd just get

\frac{-u}{u} du

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.