Stuck on the integral: arctan (4t) dt

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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.
 

Answers and Replies

  • #2
gabbagabbahey
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But when I differentiate arctan(4t), it comes out as 4t/(1+16t^2). Why is this?

Because you've calculated the derivative wrong. To tell you exactly where your error is, you'll need to post your steps.
 

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