JEE Main 2021MathematicsIndefinite IntegrationMediumNumerical

JEE Main 2021 — Indefinite Integration Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

∫2ex+3e-x4ex+7e-xdx=114ux+vloge4ex+7e-x+C, where C is a constant of integration, then u+v is equal to

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Show full solutionCorrect answer: 7
Correct answer
7

Step-by-step explanation

I=∫2ex+3e-x4ex+7e-xdx=∫2ex+34e2x+7dx
Here 2e2x+3=A8e2x+B4e2x+7
⇒2e2x+3=(8A+4B)e2x+7B
⇒B=37 & A=128
I=∫1288e2x+374e2x+74e2x+7dx
I=128ln4e2x+7+37x+C
I=128ln∣ex4ex+7e-x∣+37x+C
⇒u=132&v=12
⇒u+v=132+12=7

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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.