1
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25

Let $$\int {{{{x^{{1 \over 2}}}} \over {\sqrt {1 - {x^3}} }}dx = {2 \over 3}g(f(x)) + c}$$ ; then

(c denotes constant of integration)

A
$$f(x) = \sqrt x ,g(x) = {x^{{3 \over 2}}}$$
B
$$f(x) = {x^{{3 \over 2}}},g(x) = {\sin ^{ - 1}}x$$
C
$$f(x) = \sqrt x ,g(x) = {\sin ^{ - 1}}x$$
D
$$f(x) = {\sin ^{ - 1}}x,g(x) = {x^{{3 \over 2}}}$$
2
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
If $$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }_e}\left| {a + b\cos x} \right| + {a \over {a + b\cos x}}} \right] + c$$, then $$\alpha$$ is equal to
A
$${2 \over {{b^2}}}$$
B
$${2 \over {{a^2}}}$$
C
$$- {2 \over {{b^2}}}$$
D
$$- {2 \over {{a^2}}}$$
3
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
$$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\phi (x) - 1} }}dx = }$$
A
$${\sin ^{ - 1}} = \sqrt {{{f(x)} \over {\phi (x)}}} + c$$
B
$${\cos ^{ - 1}}\sqrt {{{(f(x))}^2} - {{(\phi (x))}^2}} + c$$
C
$$\sqrt 2 {\tan ^{ - 1}}\sqrt {{{f(x)\phi (x) - 1} \over 2}} + c$$
D
$$\sqrt 2 {\tan ^{ - 1}}\sqrt {{{f(x)\phi (x) + 1} \over 2}} + c$$
4
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
If $$\int {\cos x\log \left( {\tan {x \over 2}} \right)} dx$$ = $$\sin x\log \left( {\tan {x \over 2}} \right)$$ + f(x), then f(x) is equal to (assuming c is a arbitrary real constant).
A
c
B
c $$-$$ x
C
c + x
D
2x + c
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