JEE Main 2021MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2021 — Indefinite Integration Question with Solution

JEE Main 2021 (18 Mar Shift 1)

Question

The integral ∫(2x-1)cos(2x-1)2+54x2-4x+6dx is equal to (where c is a constant of integration)

Choose an option

Show full solutionCorrect option: A
Correct answer
A12sin(2x-1)2+5+c

Step-by-step explanation

∫(2x-1)cos(2x-1)2+5(2x-1)2+5dx

(2x-1)2+5=t2

22x-1 2dx=2 tdt

2t2-5dx=tdt

So ∫t2-5cost2t2-5dt=12sint+c

=12sin(2x-1)2+5+c

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About this question

This is a previous-year question from JEE Main 2021, 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.