1
JEE Main 2013 (Offline)
+4
-1
If $$\int {f\left( x \right)dx = \psi \left( x \right),}$$ then $$\int {{x^5}f\left( {{x^3}} \right)dx}$$ is equal to
A
$${1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} } \right] + C$$
B
$${1 \over 3}{x^3}\psi \left( {{x^3}} \right) - 3\int {{x^3}\psi \left( {{x^3}} \right)dx} + C$$
C
$${1 \over 3}{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} + C$$
D
$${1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^3}\psi \left( {{x^3}} \right)dx} } \right] + C$$
2
AIEEE 2012
+4
-1
If the $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\,\ln \,\left| {\sin x - 2\cos x} \right| + k,}$$ then $$a$$ is
equal to :
A
$$-1$$
B
$$-2$$
C
$$1$$
D
$$2$$
3
AIEEE 2008
+4
-1
The value of $$\sqrt 2 \int {{{\sin xdx} \over {\sin \left( {x - {\pi \over 4}} \right)}}}$$ is
A
$$\,x + \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
B
$$\,x - \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
C
$$\,x + \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
D
$$\,x - \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
4
AIEEE 2007
+4
-1
$$\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}}$$ equals
A
$$\log \,\tan \,\left( {{x \over 2} + {\pi \over {12}}} \right) + C$$
B
$$\log \,\tan \,\left( {{x \over 2} - {\pi \over {12}}} \right) + C$$
C
$$\,{1 \over 2}\,\log \,\tan \,\left( {{x \over 2} + {\pi \over {12}}} \right) + C$$
D
$$\,{1 \over 2}\,\log \,\tan \,\left( {{x \over 2} - {\pi \over {12}}} \right) + C$$
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