JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 2 April 2025, Shift 2, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

4\int_0^1 \left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right)\mathrm{d}x - 3\log_e(\sqrt{3})

is equal to :

(1) $2+\sqrt{2}-\log_e(1+\sqrt{2})$
(2) $2-\sqrt{2}-\log_e(1+\sqrt{2})$ Official answer
(3) $2+\sqrt{2}+\log_e(1+\sqrt{2})$
(4) $2-\sqrt{2}+\log_e(1+\sqrt{2})$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Integration by Parts
Idea tested: Roots of Quadratics via Parts

Same topic in other shifts

All Integration by Parts 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 42 of the 174 JEE Main shifts held from 2017 to 2026.