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1

IIT-JEE 1994

Subjective
Find the indefinite integral $$\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)} {\mkern 1mu} d\theta $$

Answer

$$\,\,{{\sin 2\theta } \over 2}\,ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)$$ $$ - {1 \over 2}l$$$$n\sec 2\theta + C$$
2

IIT-JEE 1992

Subjective
Find the indefinite integral $$\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x } \right)} \over {\root 3 \of x + \root \, \of x }}} \right)} dx$$

Answer

Solve it.
3

IIT-JEE 1989

Subjective
Evaluate $$\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $$

Answer

$$\sqrt 2 {\tan ^{ - 1}}\left( {{{\sqrt {\tan x} - \sqrt {\cot x} } \over {\sqrt 2 }}} \right) + C$$
4

IIT-JEE 1987

Subjective
Evaluate :$$\,\,\int {\left[ {{{{{\left( {\cos 2x} \right)}^{1/2}}} \over {\sin x}}} \right]dx} $$

Answer

$${1 \over {\sqrt 2 }}\,\log \left[ {{{\sqrt 2 + \sqrt {1 - {{\tan }^2}x} } \over {\sqrt 2 - \sqrt {1 - {{\tan }^2}x} }}} \right] - \log \left( {\cot x + \sqrt {{{\cot }^2}x - 1} } \right) + C$$

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