# Doubt from definite integration

See my final result after this i think you can integrate

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I think we can multiply and divide by some trignometric ratio to reduce into easy form

Pls check the answer...

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Nice method i was right after 2nd step i made it long

D part what is b i am not able to get cotinverse of tan^2x

if answer is 1 then there will be arctan in place of arccot or if it is in arccot then there will be cot^2x in place of tan^2x @abhijit_2020

Answer is -1

divide N^{r} and D^{r} by cos^{4}x and then put tan^{2}x = t and then integrate u will end up with tan^{-1}(tan^{2}x) and in form of arccotx it will be \pi \over 2 - cot^{-1}(tan^{2}x)