# Partial Fractions Integral

• Sep 24th 2009, 09:38 AM
Partial Fractions Integral
These partial fractions integrals have been pretty easy so far. It's really easy once you get the problem setup the correct way. I'm having trouble with this one though.

$\int \frac{3x + 2}{x^3 + 3x^2 + 3x +1}dx$
I tried factoring it but either way you end up with an extra addition on the end. Maybe there is a way to factor it so that the top reduces out?

What am I missing?

Thanks,
Justin
• Sep 24th 2009, 09:59 AM
skeeter
Quote:

These partial fractions integrals have been pretty easy so far. It's really easy once you get the problem setup the correct way. I'm having trouble with this one though.

$\int \frac{3x + 2}{x^3 + 3x^2 + 3x +1}dx$
I tried factoring it but either way you end up with an extra addition on the end. Maybe there is a way to factor it so that the top reduces out?

What am I missing?

Thanks,
Justin

$
\frac{3x + 2}{x^3 + 3x^2 + 3x +1} =
$

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

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

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

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

$\int \frac{2}{(x+1)^2} \, dx + \int \frac{u-1}{u^3} \, du$

take it from here?