# polynomial long division integral

• February 24th 2009, 02:34 PM
gammaman
polynomial long division integral
After applying polynomial long division, I arrived at the following. Based on what is here, did I do this correctly?

$\int{x^2-2x+4}+\frac{-7}{3x+1}$
$\frac{1}{3}x^3-2*\frac{1}{2}x^2+4x-7\int\frac{1}{3x+1}$
$-7ln|3x+1|+C$
• February 24th 2009, 02:38 PM
Jester
Quote:

Originally Posted by gammaman
After applying polynomial long division, I arrived at the following. Based on what is here, did I do this correctly?

$\int{x^2-2x+4}+\frac{-7}{3x+1}$
$\frac{1}{3}x^3-2*\frac{1}{2}x^2+4x-7\int\frac{1}{3x+1}$
$-7ln|3x+1|+C$

$\int \frac{-7}{3x+1}\,dx = - \frac{7}{3} \ln| 3x+1| + c$