1
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
$$\,x - \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
2
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
$$\,{1 \over 2}\,\log \,\tan \,\left( {{x \over 2} - {\pi \over {12}}} \right) + C$$
3
AIEEE 2005
+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
$${x \over {{{\left( {\log x} \right)}^2} + 1}} + C$$
4
AIEEE 2004
+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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