# Quick Integration Problem

• May 25th 2011, 06:03 PM
Status
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.
• May 25th 2011, 06:05 PM
TheEmptySet
Quote:

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.

$x^2-6x+58=(x^2-6x+9)+49=...$
• May 25th 2011, 06:08 PM
Status
Ah I got it. Thank you!
• May 25th 2011, 06:13 PM
skeeter
Quote:

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 ...

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