JEE Main 2015MathematicsIndefinite IntegrationHardMCQ

JEE Main 2015 — Indefinite Integration Question with Solution

JEE Main 2015 (11 Apr Online)

Question

If ∫logt+1+t21+t2dt=12gt2+c, where c is a constant, then g2, is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
Clog2+5

Step-by-step explanation

Put, logt+1+t2=z

⇒1t+1+t21+2t21+t2dt=dz

⇒t+1+t2 t+1+t2 11+t2dt=dz

⇒11+t2dt=dz

∴I=∫zdz=z22+c=12logt+1+t22+c, where c is the constant of integration.

∴gt=logt+1+t2

⇒g2=log2+ 1+4

Hence, log2+5, is the answer.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Indefinite Integration chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2015, 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.