JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 August 2021, Shift 2, Maths Q84

Question 84 of 90 in this shift, Maths question 24 of 30, Section B.

\int \frac{2e^x + 3e^{-x}}{4e^x + 7e^{-x}}\, dx = \frac{1}{14}\left(ux + v \log_e(4e^x + 7e^{-x})\right) + C

, where C is a constant of integration, then

u + v

is equal to __________.

Official answer

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Numerator-Denominator Derivative Matching

Same idea in other shifts

Asked 3× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.