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JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 February 2021, Shift 2, Maths Q80

Question 80 of 90 in this shift, Maths question 20 of 30, Section A.

For

x>0

, if

f(x)=\int_1^x \frac{\log_e t}{(1+t)}dt

, then

f(e)+f\left(\frac{1}{e}\right)

is equal to :

(1) $0$
(2) $1$
(3) $\frac{1}{2}$ Official answer
(4) $-1$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Reciprocal Substitution (x = 1/t)

Same idea in other shifts

Asked 2× in all

5 Apr 2026, Shift 1 · Q18The value of the integral $\int_0^{\infty} \frac{\log_e(x)}{x^2+4}\,dx$ is:HardSingle correct

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.