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

[Randall]

Homework Statement

Use the integral test to determine if this series converges or diverges: sum from n=1 to infinity of n/(1+(n^2))

Homework Equations

Integral test: a series and it's improper integral both either converge or both diverge

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.

 

[B3NR4Y]

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

 

[Randall]

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