1
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
2
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
If   $$\int {{{x + 1} \over {\sqrt {2x - 1} }}} \,dx$$ = f(x) $$\sqrt {2x - 1}$$ + C, where C is a constant of integration, then f(x) is equal to :
A
$${2 \over 3}$$ (x $$-$$ 4)
B
$${1 \over 3}$$ (x + 4)
C
$${1 \over 3}$$ (x + 1)
D
$${2 \over 3}$$ (x + 2)
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If  $$\int {{{\sqrt {1 - {x^2}} } \over {{x^4}}}}$$ dx = A(x)$${\left( {\sqrt {1 - {x^2}} } \right)^m}$$ + C, for a suitable chosen integer m and a function A(x), where C is a constant of integration, then (A(x))m equals :
A
$${1 \over {27{x^6}}}$$
B
$${{ - 1} \over {27{x^9}}}$$
C
$${1 \over {9{x^4}}}$$
D
$${1 \over {3{x^3}}}$$
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
If  $$\int \,$$x5.e$$-$$4x3 dx = $${1 \over {48}}$$e$$-$$4x3 f(x) + C, where C is a constant of inegration, then f(x) is equal to -
A
$$-$$2x3 $$-$$ 1
B
$$-$$ 2x3 + 1
C
4x3 + 1
D
$$-$$4x3 $$-$$ 1
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