`int arctan(4t) dt` Evaluate the integral

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gsarora17 eNotes educator| Certified Educator


If f(x) and g(x) are differentiable functions, then


If we write f(x)=u and g'(x)=v, then


Using the above integration by parts method,




Now let's evaluate `intt/(16t^2+1)dt`  by using the method of substitution,

Substitute `x=16t^2+1,=>dx=32tdt`



substitute back `x=16t^2+1`




C is a constant.

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