1
IIT-JEE 2006
+3
-0.75
$$\int {{{{x^2} - 1} \over {{x^3}\sqrt {2{x^4} - 2{x^2} + 1} }}dx = }$$
A
$${{\sqrt {2{x^4} - 2{x^2} + 1} } \over {{x^2}}} + c$$
B
$${{\sqrt {2{x^4} - 2{x^2} + 1} } \over {{x^3}}} + c$$
C
$${{\sqrt {2{x^4} - 2{x^2} + 1} } \over {{x}}} + c$$
D
$${{\sqrt {2{x^4} - 2{x^2} + 1} } \over {{2x^2}}} + c$$
2
IIT-JEE 2005 Screening
+3
-0.75
If $$\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,}$$ then f$$\left( {{1 \over {\sqrt 3 }}} \right)$$ is
A
$${1 \over 3}$$
B
$${{1 \over {\sqrt 3 }}}$$
C
$$3$$
D
$${\sqrt 3 }$$
3
IIT-JEE 1995 Screening
+3
-0.75
The value of the integral $$\int {{{{{\cos }^3}x + {{\cos }^5}x} \over {{{\sin }^2}x + {{\sin }^4}x}}} \,dx\,$$ is
A
$$\sin x - 6{\tan ^{ - 1}}\left( {\sin x} \right) + c$$
B
$$\sin x - 2{\left( {\sin x} \right)^{ - 1}} + c$$
C
$$\sin x - 2{\left( {\sin x} \right)^{ - 1}} - 6{\tan ^{ - 1}}\left( {\sin x} \right) + c$$
D
$$\,\sin x - 2{\left( {\sin x} \right)^{ - 1}} + 5{\tan ^{ - 1}}\left( {\sin x} \right) + c$$
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