JEE Main 2014MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2014 — Indefinite Integration Question with Solution

JEE Main 2014 (19 Apr Online)

Question

If m is a non-zero number and ∫x5m-1+2x4m-1x2m+xm+13dx=fx+c, then fx is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B12mx4mx2m+xm+12

Step-by-step explanation

∫x5m-1+2x4m-1x2m+xm+13dx=fx+c

⇒∫x5m-1+2x4m-1x6m1+x-m+x-2m3dx=fx+c

⇒∫x-m-1+2x-2m-11+x-m+x-2m3dx=fx+c.

If, 1+x-m+x-2m=t

⇒-mx-m-1+2x-2m-1dx=dt

∴∫-dtmt3=fx+c

⇒-1m∫t-3dt=fx+c

Using ∫xndx=xn+1n+1+C, n≠-1

⇒-1mt-2-2=fx+c

⇒12m1+x-m+x-2m2+c=fx+c

⇒12m1+1xm+1x2m2+c=fx+c

⇒12mx4mx2m+xm+12=fx.

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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.