JEE Main 2019MathematicsIndefinite IntegrationEasyMCQ

JEE Main 2019 — Indefinite Integration Question with Solution

JEE Main 2019 (12 Jan Shift 1)

Question

The integral ∫coslnxdx, is equal to 

Choose an option

Show full solutionCorrect option: D
Correct answer
Dx2coslnx+sinlnx+C

Step-by-step explanation

Given, I=∫coslnxdx

Let, lnx=t⇒x=et⇒dx=etdt

∴I=∫etcostdt

∫etcostdt=12∫etcost+sint+cost-sintdt

∫etcost dt=12etcost+sint+C, where C is the constant of integration.

=x2coslnx+sinlnx+C. 
 

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About this question

This is a previous-year question from JEE Main 2019, 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.