YESPYQ Start Practice
🛠️ JEE➗ Maths

Let \(I(x)=\int \frac{{x}^{2}\left(x{\sec }^{2}x+\tan x\right)}{(x\tan x+1{)}^{2}}dx\)If \(I(0)=0\) then \(I\left(\frac{…

Q1

Let \(I(x)=\int \frac{{x}^{2}\left(x{\sec }^{2}x+\tan x\right)}{(x\tan x+1{)}^{2}}dx\)If \(I(0)=0\) then \(I\left(\frac{\pi }{4}\right)\) is equal to

[JEE Main 2023, 6 Apr (Shift 1)]

a

\({\log }_{e}\frac{(\pi +4{)}^{2}}{16}-\frac{{\pi }^{2}}{4(\pi +4)}\)

b

\({\log }_{e}\frac{(\pi +4{)}^{2}}{16}+\frac{{\pi }^{2}}{4(\pi +4)}\)

c

\({\log }_{e}\frac{(\pi +4{)}^{2}}{32}-\frac{{\pi }^{2}}{4(\pi +4)}\)

d

\({\log }_{e}\frac{(\pi +4{)}^{2}}{32}+\frac{{\pi }^{2}}{4(\pi +4)}\)

🔒
Answer & explanation — PYQ Pass

Options are free to see. Unlock the correct answer and full explanation with Pass.

Unlock · ₹149
← Previous questionNext question →

Practice more JEE Maths PYQs

See every question on Indefinite Integration, or browse the full JEE question bank.

See all questions on Indefinite Integration →