Originally Posted by

**auslmar** I have this problem that needs to be solved by integration by partial fractions and I can't seem to get the right answer. Here's the problem as written:

"Find $\displaystyle \int\frac{6x+1}{20x^2+14x-12}dx$ with respect to $\displaystyle x$, use the constant $\displaystyle C$."

So, I have:

$\displaystyle

\int\frac{6x+1}{(5x+6)(4x-2)}dx = \int[\frac{A}{5x+6} + \frac{B}{4x-2}]dx

$

and

$\displaystyle

6x+1 = A(4x-2) + B(5x+6)

$

If $\displaystyle x=\frac{1}{2}$, then $\displaystyle B = \frac{8}{17}$

and

If $\displaystyle x = \frac{-6}{5}$, then $\displaystyle A = \frac{31}{850}$

So,

$\displaystyle

\int[\frac{\frac{-41}{34}}{5x+6} + \frac{\frac{8}{17}}{4x-2}]dx$

$\displaystyle

= \frac{-41}{34}ln(5x+6) + \frac{8}{17}ln(4x-2) + C

$

Unfortunately, this is not the answer. I greatly appreciate if anyone can point out where I've gone wrong. I have a feeling it was a generally small, but ultimately large, error. It is entirely possible that I have made an arthimetic mistake, by the way.

Thanks for your consideration,

Austin Martin