# Math Help - Quick Integration Problem

1. ## Quick Integration Problem

Hi,

I'm doing review problems for an upcoming exam and I'm stuck on this problem.

$\int \frac {1}{x^2-6x+58}dx$

How should I proceed? I'm guessing I have to do something to the denominator first but I'm not sure what.

Thanks for the help.

2. Originally Posted by Status
Hi,

I'm doing review problems for an upcoming exam and I'm stuck on this problem.

$\int \frac {1}{x^2-6x+58}dx$

How should I proceed? I'm guessing I have to do something to the denominator but I'm not sure what.

Thanks for the help.
Since the denominator does not factor over the reals you need to complete the square.

$x^2-6x+58=(x^2-6x+9)+49=...$

3. Ah I got it. Thank you!

4. Originally Posted by Status
Hi,

I'm doing review problems for an upcoming exam and I'm stuck on this problem.

$\int \frac {1}{x^2-6x+58}dx$

How should I proceed? I'm guessing I have to do something to the denominator first but I'm not sure what.

Thanks for the help.
note ...

$\int \frac{1}{x^2+a^2} \, dx = \frac{1}{a}\arctan\left(\frac{x}{a}\right) + C$