1

JEE Main 2023 (Online) 8th April Evening Shift

MCQ (Single Correct Answer)

+4

-1

The integral $$ \int\left[\left(\frac{x}{2}\right)^x+\left(\frac{2}{x}\right)^x\right] \ln \left(\frac{e x}{2}\right) d x $$ is equal to :

2

JEE Main 2023 (Online) 8th April Morning Shift

MCQ (Single Correct Answer)

+4

-1

Let $$I(x)=\int \frac{(x+1)}{x\left(1+x e^{x}\right)^{2}} d x, x > 0$$. If $$\lim_\limits{x \rightarrow \infty} I(x)=0$$, then $$I(1)$$ is equal to :

3

JEE Main 2023 (Online) 6th April Morning Shift

MCQ (Single Correct Answer)

+4

-1

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

4

JEE Main 2023 (Online) 25th January Morning Shift

MCQ (Single Correct Answer)

+4

-1

Let $$f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx} $$. If $$f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)$$, then $$f(4)$$ is equal to

Questions Asked from Indefinite Integrals (MCQ (Single Correct Answer))

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