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MCQ (Single Correct Answer)

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The integral $$\int {{{{{\sec }^2}x} \over {\left( {\sec x + \tan x} \right){9 \over 2}}}dx}$$ equals (for some arbitra...
IIT-JEE 2012 Paper 1 Offline
Let $$I = \int {{{{e^x}} \over {{e^{4x}} + {e^{2x}} + 1}}dx,\,\,J = \int {{{{e^{ - x}}} \over {{e^{ - 4x}} + {e^{ - 2x}}... IIT-JEE 2008 Let$$F(x)$$be an indefinite integral of$$si{n^2}x.$$STATEMENT-1: The function$$F(x)$$satisfies$$F\left( {x + \pi...
IIT-JEE 2007
$$\int {{{{x^2} - 1} \over {{x^3}\sqrt {2{x^4} - 2{x^2} + 1} }}dx = }$$
IIT-JEE 2006
If $$\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,}$$ then f$$\left( {{1 \over {\sqrt 3 }}} \right)$$ ...
IIT-JEE 2005 Screening
The value of the integral $$\int {{{{{\cos }^3}x + {{\cos }^5}x} \over {{{\sin }^2}x + {{\sin }^4}x}}} \,dx\,$$ is
IIT-JEE 1995 Screening

Subjective

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For any natural number $$m$$, evaluate $$\int {\left( {{x^{3m}} + {x^{2m}} + {x^m}} \right){{\left( {2{x^{2m}} + 3{x^m} ... IIT-JEE 2002 Evaluate$$\int {{{\sin }^{ - 1}}\left( {{{2x + 2} \over {\sqrt {4{x^2} + 8x + 13} }}} \right)} \,dx.$$IIT-JEE 2001 Integrate$$\int {{{{x^3} + 3x + 2} \over {{{\left( {{x^2} + 1} \right)}^2}\left( {x + 1} \right)}}dx.} $$IIT-JEE 1999 Evaluate$$\int {{{\left( {x + 1} \right)} \over {x{{\left( {1 + x{e^x}} \right)}^2}}}dx} $$. IIT-JEE 1996 Find the indefinite integral$$\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \t...
IIT-JEE 1994
Find the indefinite integral $$\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x... IIT-JEE 1992 Evaluate$$\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $$IIT-JEE 1989 Evaluate :$$\,\,\int {\left[ {{{{{\left( {\cos 2x} \right)}^{1/2}}} \over {\sin x}}} \right]dx} $$IIT-JEE 1987 Evaluate the following$$\int {\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}dx} } $$IIT-JEE 1985 Evaluate the following$$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} $$IIT-JEE 1984 Evaluate :$$\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx} $$IIT-JEE 1983 Evaluate$$\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.} $$IIT-JEE 1981 Evaluate$$\int {{{{x^2}dx} \over {{{\left( {a + bx} \right)}^2}}}} $$IIT-JEE 1979 Evaluate$$\int {{{\sin x} \over {\sin x - \cos x}}dx} $$IIT-JEE 1978 Fill in the Blanks More If$$\int {{{4{e^x} + 6{e^{ - x}}} \over {9{e^x} - 4{e^{ - x}}}}\,dx = Ax + B\,\,\log \left( {9{e^{2x}} - 4} \right) + C...
IIT-JEE 1990

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