JEE Main 2016MathematicsIndefinite IntegrationHardMCQ

JEE Main 2016 — Indefinite Integration Question with Solution

JEE Main 2016 (10 Apr Online)

Question

The integral ∫dx1+xx-x2 is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C-2 1-x1+x+c

Step-by-step explanation

I=∫dx1+xx1-x

Put, 1+x=t ⇒12xdx=dt

And, 1-x=1-t-12=2t-t2

∴ I= ∫2dtt2t-t2

Again put, t=1z⇒dt=-1z2dz

⇒I=2∫-1z2 dz1z 2z-1z2=2∫-dz2z-1=-22z-1+c

Where c is arbitrary constant.

=-22t-1 +c

=-22-tt+c

=-2 1-x1+x+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.