JEE Main 2023MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2023 — Indefinite Integration Question with Solution

JEE Main 2023 (25 Jan Shift 1)

Question

Let fx=∫2xx2+1x2+3dx. If f3=12loge5-loge6, then f4 is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A12loge17-logc19

Step-by-step explanation

Let

I=∫2xx2+1x2+3dx

Put x2=t⇒2xdx=dt

I=∫1t+1t+3dt

⇒I=12∫2t+1t+3dt

⇒I=12∫1t+1-1t+3dt

⇒I=12lnt+1-lnt+3+C

⇒fx=12lnx2+1-lnx2+3+C

Put x=3, then

12ln5-ln6=12ln10-ln12+C

12ln5-ln6=12ln2+ln5-ln2-ln6+C

⇒C=0

So,

fx=12lnx2+1-lnx2+3

⇒f4=12ln17-ln19 or f4=12loge17-loge19

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About this question

This is a previous-year question from JEE Main 2023, 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.