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1

IIT-JEE 1983

Subjective
Evaluate : $$\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx} $$

Answer

$${{{e^x}} \over {{{\left( {x + 1} \right)}^2}}} + C$$
2

IIT-JEE 1981

Subjective
Evaluate $$\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.} $$

Answer

$$x\sin x + \cos x - {1 \over 4}\cos 2x + C$$
3

IIT-JEE 1979

Subjective
Evaluate $$\int {{{{x^2}dx} \over {{{\left( {a + bx} \right)}^2}}}} $$

Answer

$${1 \over {{b^3}}}\left[ {a + bx - 2a\log \left| {a + bx} \right| - {{{a^2}} \over {a + bx}}} \right] + C$$
4

IIT-JEE 1978

Subjective
Evaluate $$\int {{{\sin x} \over {\sin x - \cos x}}dx} $$

Answer

$${1 \over 2}\log \left| {\sin x - \cos x} \right| + {x \over 2} + C$$

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Class 12