JEE Main 2018MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2018 — Indefinite Integration Question with Solution

JEE Main 2018 (16 Apr Online)

Question

If ∫tanx1+tanx+tan2xdx=x-KAtan-1Ktanx+1A+C, (C is a constant of integration), then the ordered pair K,A is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B2,3

Step-by-step explanation

Let I=∫tanx1+tanx+tan2xdx

⇒I=∫1-sec2x1+tanx+tan2xdx

⇒I=x-∫dt1+t+t2

Where, tanx=t⇒sec2xdx=dt

∴ I=x-132tan-1t+1232+C, where C is the constant of integration.

=x-23tan-12tanx+13+C

∴ K=2 & A=3.

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About this question

This is a previous-year question from JEE Main 2018, 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.