JEE Main 2016MathematicsIndefinite IntegrationHardMCQ

JEE Main 2016 — Indefinite Integration Question with Solution

JEE Main 2016 (03 Apr)

Question

The integral ∫2x12+5x9x5+x3+13dx, is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
Dx102x5+x3+12+c

Step-by-step explanation

Given, I=∫2x12+5x9x5+x3+13dx

=∫2x12+5x9dxx151+1x2+1x53

=∫2x3+5x6dx1+1x2+1x53

Let, 1+1x2+1x5=t ⇒-2x3-5x6dx=dt

⇒2x3+5x6dx=-dt

I=-∫dtt3=12 . t2

I=1211+1x2+1x52+c=12x10x5+x3+12+c
Where c is the constant of integration.
=x102x5+x3+12+c

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About this question

This is a previous-year question from JEE Main 2016, 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.