1
WB JEE 2009
+1
-0.25

$$\int {{{dx} \over {\sin x + \sqrt 3 \cos x}}}$$ equals

A
$${1 \over 2}\ln \left| {\tan \left( {{x \over 2} - {\pi \over 6}} \right)} \right| + c$$
B
$${1 \over 2}\ln \left| {\tan \left( {{x \over 4} - {\pi \over 6}} \right)} \right| + c$$
C
$${1 \over 2}\ln \left| {\tan \left( {{x \over 2} + {\pi \over 6}} \right)} \right| + c$$
D
$${1 \over 2}\ln \left| {\tan \left( {{x \over 4} + {\pi \over 6}} \right)} \right| + c$$
2
WB JEE 2009
+1
-0.25

$$\int {{{{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx}$$ equal to

where c is an arbitrary constant

A
$$\log ({\sin ^{ - 1}}x) + c$$
B
$${1 \over 2}{({\sin ^{ - 1}}x)^2} + c$$
C
$$\log \left( {\sqrt {1 - {x^2}} } \right) + c$$
D
$$\sin ({\cos ^{ - 1}}x) + c$$
3
WB JEE 2010
+1
-0.25

$$\int {{{\log \sqrt x } \over {3x}}dx}$$ is equal to

A
$${1 \over 3}{\left( {\log \sqrt x } \right)^2} + C$$
B
$${2 \over 3}{\left( {\log \sqrt x } \right)^2} + C$$
C
$${2 \over 3}{\left( {\log x} \right)^2} + C$$
D
$${1 \over 3}{\left( {\log x} \right)^2} + C$$
4
WB JEE 2010
+1
-0.25

$$\int {{e^x}\left( {{2 \over x} - {2 \over {{x^2}}}} \right)dx}$$ is equal to

A
$${{{e^x}} \over x} + C$$
B
$${{{e^x}} \over {2{x^2}}} + C$$
C
$${{2{e^x}} \over x} + C$$
D
$${{2{e^x}} \over {{x^2}}} + C$$
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