1
WB JEE 2020
+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
$$\sqrt 2 {\tan ^{ - 1}}\sqrt {{{f(x)\phi (x) + 1} \over 2}} + c$$
2
WB JEE 2019
+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
3
WB JEE 2019
+1
-0.25
y = $$\int {\cos \left\{ {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right\}} dx$$ is an equation of a family of
A
straight lines
B
circles
C
ellipses
D
parabolas
4
WB JEE 2019
+1
-0.25
If $$\int {{2^{{2^x}}}.\,{2^x}dx} = A\,.\,{2^{{2^x}}} + C$$, then A is equal to
A
$${1 \over {\log 2}}$$
B
log 2
C
$${{{(\log 2)}^2}}$$
D
$${1 \over {{{(\log 2)}^2}}}$$
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NEET