1
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
If $$\int {{{dx} \over {{x^3}{{(1 + {x^6})}^{2/3}}}} = xf(x){{(1 + {x^6})}^{{1 \over 3}}} + C}$$
where C is a constant of integration, then the function ƒ(x) is equal to
A
$${3 \over {{x^2}}}$$
B
$$- {1 \over {6{x^3}}}$$
C
$$- {1 \over {2{x^3}}}$$
D
$$- {1 \over {2{x^2}}}$$
2
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
$$\int {{{\sin {{5x} \over 2}} \over {\sin {x \over 2}}}dx}$$ is equal to
(where c is a constant of integration)
A
2x + sinx + 2sin2x + c
B
x + 2sinx + sin2x + c
C
x + 2sinx + 2sin2x + c
D
2x + sinx + sin2x + c
3
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
The integral $$\int {{{3{x^{13}} + 2{x^{11}}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^4}}}} \,dx$$ is equal to : (where C is a constant of integration)
A
$${{{x^{12}}} \over {6{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}}$$ + $$C$$
B
$${{{x^4}} \over {6{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C$$
C
$${{{x^{12}}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C$$
D
$${{{x^4}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C$$
4
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
The integral $$\int \,$$cos(loge x) dx is equal to : (where C is a constant of integration)
A
$${x \over 2}$$[sin(loge x) $$-$$ cos(loge x)] + C
B
x[cos(loge x) + sin(loge x)] + C
C
$${x \over 2}$$[cos(loge x) + sin(loge x)] + C
D
x[cos(loge x) $$-$$ sin(loge x)] + C
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