The Integral is arctan (4t) dt
I know how to do integration by parts, but I guess I have forgotten some of the integration rules.
The Attempt at a Solution
I set ∫arctan(4t)=u, and dt=dv
I know that the derivative of arctan(x) is 1/(1+x^2), But when I differentiate arctan(4t), it comes out as 4t/(1+16t^2). Why is this? To me it seems like it should be 1/(1+4t^2). I know how to do the rest, I have the answer, I'm just not sure how they got there. Thanks for any help.