JEE Main 2014MathematicsIndefinite IntegrationHardMCQ

JEE Main 2014 — Indefinite Integration Question with Solution

JEE Main 2014 (06 Apr)

Question

The integral ∫1+x-1xex+1xdx, is equal to 

Choose an option

Show full solutionCorrect option: D
Correct answer
Dxex+1x+c

Step-by-step explanation

∫1+x-1xex+1xdx=∫ex+1xdx+∫x1-1x2ex+1xdx

Integrating ∫x⏟I.(1−1x2)ex+1x⏟IIdx, by parts

I=xex+1x-∫ex+1xdx+c

=∫1+x-1xex+1xdx=∫ex+1xdx+xex+1x-∫ex+1xdx+c

=xex+1x+c, where c is the constant of integration.  

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About this question

This is a previous-year question from JEE Main 2014, 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.