# Thread: Partial fractions and integration

1. ## Partial fractions and integration

$\displaystyle \int\frac{x+2}{(x+3)^2(x+1)}$

2. Get a CAS.

3. Thanks for the quick reply. What's a CAS?

Darn, my first time using Latex and I forgot to put in the limits which was 3 and 0. Anyhow my partial fractions matches yours, but my answer(ln 8) after integrating doesn't match the answer page of my book.

4. Originally Posted by gamboo
$\displaystyle \int\frac{x+2}{(x+3)^2(x+1)}$
$\displaystyle \int\frac{x+2}{(x+3)^2(x+1)}dx = \frac{1}{2}\int\frac{(x+3) +(x+1)}{(x+3)^2(x+1)} dx =$ $\displaystyle \frac{1}{2} \int \frac{1}{(x+3)(x+1)} dx + \frac{1}{2} \int \frac{1}{(x+3)^2} \,dx$ $\displaystyle = \frac{1}{4} \int \frac{(x+3)-(x+1)}{(x+3)(x+1)} dx + \frac{1}{2} \int \frac{1}{(x+3)^2} \,dx$

$\displaystyle = \frac{1}{4} \int \frac{dx}{x+1} - \frac{1}{4} \int \frac{dx}{x+4} + \frac{1}{2} \int \frac{dx}{(x+3)^2}$

Originally Posted by gamboo
Thanks for the quick reply. What's a CAS?

Darn, my first time using Latex and I forgot to put in the limits which was 3 and 0. Anyhow my partial fractions matches yours, but my answer(ln 8) after integrating doesn't match the answer page of my book.
Computer Algebra System (CAS)