JEE Main 2022 (Online) 26th June Evening Shift | Indefinite Integrals Question 20 | Mathematics

JEE Main 2022 (Online) 26th June Evening Shift

MCQ (Single Correct Answer)

-1

If $$\int {{1 \over x}\sqrt {{{1 - x} \over {1 + x}}} dx = g(x) + c} $$, $$g(1) = 0$$, then $$g\left( {{1 \over 2}} \right)$$ is equal to :

$${\log _e}\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right) + {\pi \over 3}$$

$${\log _e}\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right) + {\pi \over 3}$$

$${\log _e}\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right) - {\pi \over 3}$$

$${1 \over 2}{\log _e}\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right) - {\pi \over 6}$$

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

The integral $$\int {{1 \over {\root 4 \of {{{(x - 1)}^3}{{(x + 2)}^5}} }}} \,dx$$ is equal to : (where C is a constant of integration)

$${3 \over 4}{\left( {{{x + 2} \over {x - 1}}} \right)^{{1 \over 4}}} + C$$

$${3 \over 4}{\left( {{{x + 2} \over {x - 1}}} \right)^{{5 \over 4}}} + C$$

$${4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{{1 \over 4}}} + C$$

$${4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{{5 \over 4}}} + C$$

JEE Main 2021 (Online) 18th March Morning Shift

MCQ (Single Correct Answer)

-1

The integral $$\int {{{(2x - 1)\cos \sqrt {{{(2x - 1)}^2} + 5} } \over {\sqrt {4{x^2} - 4x + 6} }}} dx$$ is equal to (where c is a constant of integration)

$${1 \over 2}\sin \sqrt {{{(2x - 1)}^2} + 5} + c$$

$${1 \over 2}\cos \sqrt {{{(2x + 1)}^2} + 5} + c$$

$${1 \over 2}\cos \sqrt {{{(2x - 1)}^2} + 5} + c$$

$${1 \over 2}\sin \sqrt {{{(2x + 1)}^2} + 5} + c$$

JEE Main 2021 (Online) 25th February Evening Shift

MCQ (Single Correct Answer)

-1

The integral $$\int {{{{e^{3{{\log }_e}2x}} + 5{e^{2{{\log }_e}2x}}} \over {{e^{4{{\log }_e}x}} + 5{e^{3{{\log }_e}x}} - 7{e^{2{{\log }_e}x}}}}} dx$$, x > 0, is equal to : (where c is a constant of integration)

$${\log _e}\sqrt {{x^2} + 5x - 7} + c$$

$$4{\log _e}|{x^2} + 5x - 7| + c$$

$${1 \over 4}{\log _e}|{x^2} + 5x - 7| + c$$

$${\log _e}|{x^2} + 5x - 7| + c$$

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