JEE Main 2021MathematicsIndefinite IntegrationHardNumerical

JEE Main 2021 — Indefinite Integration Question with Solution

JEE Main 2021 (16 Mar Shift 2)

Question

For real numbers α,β,γ and δ, if ∫x2-1+tan-1x2+1xx4+3x2+1tan-1x2+1xdx=αlogetan-1x2+1x+βtan-1γx2-1x+δtan-1x2+1x+C  where C is an arbitrary constant, then the value of 10(α+βγ+δ) is equal to ______ .

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Show full solutionCorrect answer: 6
Correct answer
6

Step-by-step explanation

∫x2-1dxx4+3x2+1tan-1x+1x+∫dxx4+3x2+1

∫1-1x2dxx+1x2+1tan-1x+1x+12∫x2+1-x2-1dxx4+3x2+1

Put tan-1x+1x=t

∫dtt+12∫1+1x2dxx-1x2+5-12∫1-1x2dxx+1x2+1

Put x-1x=y,x+1x=z

loget+12∫dyy2+5-12∫dzz2+1

=logetan-1x+1x+125tan-1x2-15x

-12tan-1x2+1x+C

α=1,β=125,γ=15,δ=-12

or α=1,β=-125,γ=-15,δ=-12

10(α+βγ+δ)=101+110-12=6

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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.