JEE Main 2021MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2021Indefinite Integration Question with Solution

JEE Main 2021 (25 Feb Shift 2)

Question

The integral e3loge2x+5e2loge2xe4logex+5e3logex-7e2logex dx, x>0, is equal to
(where c is a constant of integration)

Choose an option

Show full solutionCorrect option: B
Correct answer
B4logex2+5x-7+c

Step-by-step explanation

e3loge2x+5e2loge2xe4logex+5e3logex-7e2logexdx,x>0

=2x3+52x2x4+5x3-7x2dx=4x22x+5x2x2+5x-7dx

=4dx2+5x-7x2+5x-7=4logex2+5x-7+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.