It's been a while since I did integrals, and i'm having trouble with this problem.
∫√( (2t)^2 + (t^-2) + (4) ) And the integral goes from 1 to e
Is there an easier way I can simplify the stuff under the square root, in order to make this less messy? Or do I have to go straight to substitution? And if so, whats the best way to start? Thanks for your time.
first of all, the 1st term inside the root is it (2t)^2 or just 2t^2, if there is a bracket round 2t then you have to make it to 4t^2
edit: wait, my mistake I'm just being stupid lol
Now when I take the integral of (2t^2 + 1) / t from 1 to e
I simplified it to ∫ 2t^2 / t + 1/t dt -----> ∫2t + t^-1 dt
But I have a problem with the "t^-1" term when I take the anti-derivative of it. It comes out as t^0 / 0 which cant be right. Did i simplify this wrong?