Integrating by Parts: Showing $\int \frac{1}{1-x^2}dx$

[thereddevils]

Homework Statement

By integrating by parts , show that

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

Homework Equations

The Attempt at a Solution

I don see which is u and v.

 

[Cyosis]

You can view the first integral as a product of two functions, which ones? Now if you don't see which one should be u and which one should be v just try one. After all there are only two possibilities.

 

[Tedjn]

Perhaps it would further help to think about how the x could appear in the numerator of the first term on the right hand side.