JEE Main 2021MathematicsIndefinite IntegrationHardNumerical

JEE Main 2021 — Indefinite Integration Question with Solution

JEE Main 2021 (27 Aug Shift 1)

Question

If ∫dxx2+x+12=atan-12x+13+b2x+1x2+x+1+C, x>0 where C is the constant of integration, then the value of 9(3a+b) is equal to _________.

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Show full solutionCorrect answer: 15
Correct answer
15

Step-by-step explanation

I=∫dxx+122+342

Put x+12=t

=∫dtt2+342

  Put  t=32tan θ=32∫sec2θ dθ916sec4θ    

=439∫1+cos 2θdθ

=439θ+sin 2θ2+C

=439tan-12x+13+32x+13+2x+12+C

=439tan-12x+13+132x+1x2+x+1+C

Hence, 93a+b=15

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About this question

This is a previous-year question from JEE Main 2021, 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.