## Integration problem

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

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

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?
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 Recognitions: Homework Help If u^2=1-x^2 2u du =-2x dx => - u du = x dx Now you'd just get $$\frac{-u}{u} du$$
 ok got it, thank you

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## Integration problem

 Quote by rock.freak667 If u^2=1-x^2 2u du =-2x dx => - u du = x dx Now you'd just get $$\frac{-u}{u} du$$
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.

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