1
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
$$\int {{e^{\sec x}}}$$ $$(\sec x\tan xf(x) + \sec x\tan x + se{x^2}x)dx$$
= esecxf(x) + C then a possible choice of f(x) is :-
A
x sec x + tan x + 1/2
B
sec x + xtan x - 1/2
C
sec x - tan x - 1/2
D
sec x + tan x + 1/2
2
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
3
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
$$- {1 \over {2{x^2}}}$$
4
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
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