JEE Main 2021MathematicsIndefinite IntegrationHardMCQ

JEE Main 2021 — Indefinite Integration Question with Solution

JEE Main 2021 (31 Aug Shift 1)

Question

The integral ∫1(x-1)3(x+2)54 dx is equal to : (where C is a constant of integration)

Choose an option

Show full solutionCorrect option: B
Correct answer
B43x-1x+214+C

Step-by-step explanation

I=∫dx(x-1)3(x+2)54

I=∫dx(x-1)34(x+2)54

I=∫dx(x-1)2x+2x-154

Let x+2x-1 =t

Differentiate on both sides

x-1-x+2x-12.dx = dt

⇒dxx-12 = -dt3

I=-13∫dtt54

= -13t-54+11-54+C

=43t-14+C

=431t14+C

= 43x-1x+214+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.