JEE Main 2024MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2024 — Indefinite Integration Question with Solution

JEE Main 2024 (27 Jan Shift 2)

Question

The integral ∫x8-x2dxx12+3x6+1tan-1x3+1x3 is equal to :

Choose an option

Show full solutionCorrect option: A
Correct answer
Alogtan-1x3+1x313+C

Step-by-step explanation

Let, I=∫x8-x2x12+3x6+1tan-1x3+1x3dx

Putting, tan-1x3+1x3=t

⇒11+x3+1x32·3x2-3x4dx=dt

⇒11+x6+1x6+2·3x2-3x4dx=dt

⇒x6x12+3x6+1·3x6-3x4dx=dt

⇒x8-x2x12+3x6+1dx=dt3

⇒I=13∫1tdt

⇒I=13log|t|+C

⇒I=13logtan-1x3+1x3+C

⇒I=logtan-1x3+1x313+C

Hence optin A is correct

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About this question

This is a previous-year question from JEE Main 2024, 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.