1. The problem statement, all variables and given/known data evaluate the integral 1/(u^2 -36) from 0 to 6 does the integral converge? 2. Relevant equations 3. The attempt at a solution integral 1/(u^2 -36) integral 1/((u-6)(u+6)) Partial fraction decomposition 1/((u-6)(u+6)) = A/(u-6) + B/(u+6) 1=A(u+6) + B(u-6) 1=(A+B)u +(6A-6B) A+B=0 A=-B 6A -6B=1 -12B=1 B=-1/12 A=1/12 1/12 int 1/(y-6) - 1/12 int 1/(y+6) 1/12 ln|y-6| - 1/12 ln|y+6| I'm being told however by wolframalpha that it should be 1/12 ln|6-y| - 1/12 ln|y+6| How did that happen? I also wanted to try to use the comparison theorem to see if it converges or not. I use the function g(x)=1/y^2 and i know that does not converge from 0 to 6, and since it is larger than f(x) then f(x) also does not converge. Did i go about that correctly?