JEE Main 2023MathematicsIndefinite IntegrationHardMCQ

JEE Main 2023 — Indefinite Integration Question with Solution

JEE Main 2023 (08 Apr Shift 2)

Question

The integral ∫x2x+2xxlog2x dx is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
Ax2x+2xx+C

Step-by-step explanation

Given,

I=∫x2x+2xxlog2x dx

Now, Let x2x=t

⇒  xlog2x2=log2t

⇒  xlogex2·log2e=loget·log2e

On differentiating both sides we get :
logex2+x·2x·12=1tdtdx

⇒logex2+1=1tdtdx

Then solution is not possible as there is no proper substitution.

Note: This question was bonus in Jee Mains 2023 April session.

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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.