JEE Main 2023MathematicsIndefinite IntegrationMediumMCQ

JEE Main 2023 — Indefinite Integration Question with Solution

JEE Main 2023 (13 Apr Shift 1)

Question

∫0∞6e3x+6e2x+11ex+6dx=

Choose an option

Show full solutionCorrect option: A
Correct answer
Aloge3227

Step-by-step explanation

Let

I=∫0∞6e3x+6e2x+11ex+6dx

⇒I=∫0∞6ex+1ex+2ex+3dx

Using partial fraction, we can write

⇒I=6∫0∞12ex+1-1ex+2+12ex+3dx

⇒I=6∫0∞12e-x+1-11+2e-x+121+3e-xe-xdx

⇒I=6-12logee-x+1+12loge2e-x+1-16loge3e-x+10∞

⇒I=60--12loge2+12loge3-16loge4

⇒I=3loge2-3loge3+loge4

⇒I=5loge2-3loge3

⇒I=loge3227

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 2023, 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.