1
JEE Main 2015 (Offline)
+4
-1
The integral $$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}}$$ equals :
A
$$- {\left( {{x^4} + 1} \right)^{{1 \over 4}}} + c$$
B
$$- {\left( {{{{x^4} + 1} \over {{x^4}}}} \right)^{{1 \over 4}}} + c$$
C
$${\left( {{{{x^4} + 1} \over {{x^4}}}} \right)^{{1 \over 4}}} + c$$
D
$${\left( {{x^4} + 1} \right)^{{1 \over 4}}} + c$$
2
JEE Main 2014 (Offline)
+4
-1
The integral $$\int {\left( {1 + x - {1 \over x}} \right){e^{x + {1 \over x}}}dx}$$ is equal to
A
B
C
D
3
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
$${1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^3}\psi \left( {{x^3}} \right)dx} } \right] + C$$
4
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
$$2$$
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