JEE Main 2019 (Online) 8th April Evening Slot | Indefinite Integrals Question 47 | Mathematics

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

$${3 \over {{x^2}}}$$

$$ - {1 \over {6{x^3}}}$$

$$ - {1 \over {2{x^3}}}$$

$$ - {1 \over {2{x^2}}}$$

JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

$$\int {{{\sin {{5x} \over 2}} \over {\sin {x \over 2}}}dx} $$ is equal to
(where c is a constant of integration)

2x + sinx + 2sin2x + c

x + 2sinx + sin2x + c

x + 2sinx + 2sin2x + c

2x + sinx + sin2x + c

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-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)

$${{{x^{12}}} \over {6{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}}$$ + $$C$$

$${{{x^4}} \over {6{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C$$

$${{{x^{12}}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C$$

$${{{x^4}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C$$

JEE Main 2019 (Online) 12th January Morning Slot

MCQ (Single Correct Answer)

-1

The integral $$\int \, $$cos(log_e x) dx is equal to : (where C is a constant of integration)

$${x \over 2}$$[sin(log_e x) $$-$$ cos(log_e x)] + C

x[cos(log_e x) + sin(log_e x)] + C

$${x \over 2}$$[cos(log_e x) + sin(log_e x)] + C

x[cos(log_e x) $$-$$ sin(log_e x)] + C