JEE Main 2019MathematicsIndefinite IntegrationHardMCQ

JEE Main 2019 — Indefinite Integration Question with Solution

JEE Main 2019 (12 Apr Shift 2)

Question

Let α∈(0,π2) , be constant.If the integral ∫tanx+tanαtanx-tanαdx=Axcos2α+Bxsin2α+C, where C is a constant of integration, then the functions A(x) and B(x) are respectively
 

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Show full solutionCorrect option: A
Correct answer
Ax-α and logesinx-α

Step-by-step explanation

I=∫tanx+tanαtanx-tanαdx=∫sinxcosx+sinαcosαsinxcosx-sinαcosαdx
=∫sinxcosα+cosxsinαsinxcosα-cosxsinαdx=∫sinx+αsinx-αdx
=∫sinx-α+2αsin(x-α)dx=∫sinx-αcos2α+cosx-αsin2αsin(x-α)dx
=∫cos2α+sin2αcotx-αdx
=xcos2α+sin2αlogesinx-α+C
=(x-α)cos2α+sin2αlogesinx-α+C
Hence, Ax=x-α and Bx=logesinx-α

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About this question

This is a previous-year question from JEE Main 2019, covering the Indefinite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.