Evaluating Integral with Partial Fractions: A Numerical Approach

[colderduck]

Homework Statement

I am supposed to evaluate the integral using partial fractions.
\int \frac{1}{(x+5)^2(x-1)} dx

2. The attempt at a solution

So after doing all the work, I get
(-1/36)ln|x+5| - (13/6)ln|x+5| + (1/36)ln|x-1|

But the answer in the book appears as
(-1/36)ln|x+5| - (1/6)\frac{1}{x+5} + (1/36)ln|x-1|

Here is what I have before I integrate it.
\int \frac{-1/36}{x+5} - \frac{1/6}{(x+5)^2} + \frac{1/36}{x-1} dx
I assume it has to do with the (x+5)², but I can't figure out what happened to get that.

 

[Gib Z]

Well, there's some sort of sign error involving the term we are concerned with, but disregarding that, the books answer is correct.

What is the antiderivative of 1/x^2 ? I don't see where you pulled a log from.

Welcome to PF btw =] !

 

[HallsofIvy]

Homework Statement

I am supposed to evaluate the integral using partial fractions.
\int \frac{1}{(x+5)^2(x-1)} dx

2. The attempt at a solution

So after doing all the work, I get
(-1/36)ln|x+5| - (13/6)ln|x+5| + (1/36)ln|x-1|

But the answer in the book appears as
(-1/36)ln|x+5| - (1/6)\frac{1}{x+5} + (1/36)ln|x-1|

Here is what I have before I integrate it.
\int \frac{-1/36}{x+5} - \frac{1/6}{(x+5)^2} + \frac{1/36}{x-1} dx
I assume it has to do with the (x+5)², but I can't figure out what happened to get that.

Please show how you got that. What partial fractions did you get and how did you integrate each?