JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 February 2021, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

The integral

\int \frac{e^{3\log_e 2x} + 5e^{2\log_e 2x}}{e^{4\log_e x} + 5e^{3\log_e x} - 7e^{2\log_e x}} \, dx

x > 0

, is equal to : (where c is a constant of integration)

(1) $\log_e|x^2+5x-7| + c$
(2) $4\log_e|x^2+5x-7| + c$ Official answer
(3) $\frac{1}{4}\log_e|x^2+5x-7| + c$
(4) $\log_e\sqrt{x^2+5x-7} + c$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Logarithmic Derivative Integration Rule

Same topic in other shifts

All Integration by Substitution questions

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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.