Integration by parts possible?

[Krappy]

Homework Statement

Calculate:

$$\integral \frac{1}{(x^2+1)(x+1)}$$

Homework Equations

$$\integral f(x) g'(x) = f(x) g(x) - \integral f'(x) g(x) + C$$

The Attempt at a Solution

I've tried using both $$1/(x+1)$$ and $$1/(x^2 + 1)$$ as $$dv$$, but both end up in another integral I can't solve, one with $$-ln(x+1) 2x / (x^2+1)^2$$ and the other with $$-atan(x)/(x+1)^2$$.

I think that probably this can only be solved with the method for rational functions (with all the coefficients), but I'm not sure.

 

[Dick]

Using partial fractions is much better idea.

 

[Krappy]

Using partial fractions is much better idea.

Thanks for answering. I know it's much better, but I'm solving some tests (same format) and the position in which this one appears is the "integration by parts question".