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1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
$$\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx} $$ is equal to
A
$${{\log x} \over {{{\left( {\log x} \right)}^2} + 1}} + C$$
B
$${x \over {{x^2} + 1}} + C$$
C
$${{x{e^x}} \over {1 + {x^2}}} + C$$
D
$${x \over {{{\left( {\log x} \right)}^2} + 1}} + C$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
$$\int {{{dx} \over {\cos x - \sin x}}} $$ is equal to
A
$${1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} + {{3\pi } \over 8}} \right)} \right| + C$$
B
$${1 \over {\sqrt 2 }}\log \left| {\cot \left( {{x \over 2}} \right)} \right| + C$$
C
$${1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} - {{3\pi } \over 8}} \right)} \right| + C$$
D
$$\,{1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} - {\pi \over 8}} \right)} \right| + C$$
3
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If $$\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,} $$ then value of
$$(A, B)$$ is
A
$$\left( { - \cos \alpha ,\sin \alpha } \right)$$
B
$$\left( { \cos \alpha ,\sin \alpha } \right)$$
C
$$\left( { - \sin \alpha ,\cos \alpha } \right)$$
D
$$\left( { \sin \alpha ,\cos \alpha } \right)$$
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