1
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
The integral $$\int {{\rm{se}}{{\rm{c}}^{{\rm{2/ 3}}}}\,{\rm{x }}\,{\rm{cose}}{{\rm{c}}^{{\rm{4 / 3}}}}{\rm{x \,dx}}}$$ is equal to (Hence C is a constant of integration)
A
-3/4 tan - 4 / 3 x + C
B
3tan–1/3x + C
C
–3cot–1/3x+ C
D
- 3tan–1/3x + C
2
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
$$- {1 \over {2{x^2}}}$$
3
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
4
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
$${{{x^4}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C$$
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