Stuck on the integral: arctan (4t) dt

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SUMMARY

The integral of arctan(4t) dt requires the application of integration by parts and an understanding of the chain rule for differentiation. The derivative of arctan(4t) is correctly calculated as 4/(1 + (4t)^2), which simplifies to 4t/(1 + 16t^2). The confusion arises from misapplying the derivative formula for arctan(x), leading to incorrect assumptions about the integration process. Clear steps in differentiation are crucial for accurate integration.

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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.
 
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dlikes said:
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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