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## Homework Statement

The Integral is arctan (4t) dt

## Homework Equations

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.