# Thread: Evaluating an integral

1. ## Evaluating an integral

$\displaystyle \int_{1}^{3} \frac{dx}{x(x+1)^2}$

I can't seem to come across a solution, any ideas?

2. partial fractions

$\displaystyle \frac{1}{x(x+1)^2}= { a\over x}+{ b\over x+1}+{ c\over (x+1)^2}$

3. I'm sorry, I should have been more clear, but I just recently "learned" how to do these type of problem. I haven't really been able to apply it though. Could you please help me through with a step by step sort of approach?

4. Originally Posted by looseenz2
I'm sorry, I should have been more clear, but I just recently "learned" how to do these type of problem. I haven't really been able to apply it though. Could you please help me through with a step by step sort of approach?
Partial-Fraction Decomposition: General Techniques

5. this is how you avoid partial fractions to save time:

put $\displaystyle x=\frac1t$ and the integral becomes $\displaystyle \int_{\frac13}^1\frac t{(t+1)^2}\,dt$ now substitute $\displaystyle u=t+1$ and the integral becomes $\displaystyle \int_{\frac43}^2\frac{u-1}{u^2}\,du,$ thus the rest should be pretty easy.

6. I have tried to learn it through various websites, it's just hard for me to grasp for some reason, but thanks anyway