# Use the integral test to determine if this series converges or diverges

1. Jan 2, 2015

### Randall

1. The problem statement, all variables and given/known data
Use the integral test to determine if this series converges or diverges: sum from n=1 to infinity of n/(1+(n^2))
2. Relevant equations
Integral test: a series and it's improper integral both either converge or both diverge

3. The attempt at a solution
see attached - I need help finding the integral. I tried using an online integral calculator, symbolab but it says there is no integral. I'm guessing there is some way to split this up into pieces that I'm not seeing. Please help.

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2. Jan 2, 2015

### B3NR4Y

Your proof that it is positive and decreasing isn't sufficient, but the integral is fairly trivial. U-substitution comes to mind.

3. Jan 2, 2015

### Randall

Thank you! Yes I used substitution and got it to work :)