JEE Main 2019 (Online) 12th January Evening Slot | Indefinite Integrals Question 49 | Mathematics

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

JEE Main 2019 (Online) 11th January Evening Slot

MCQ (Single Correct Answer)

-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 :

$${2 \over 3}$$ (x $$-$$ 4)

$${1 \over 3}$$ (x + 4)

$${1 \over 3}$$ (x + 1)

$${2 \over 3}$$ (x + 2)

JEE Main 2019 (Online) 11th January Morning Slot

MCQ (Single Correct Answer)

-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 :

$${1 \over {27{x^6}}}$$

$${{ - 1} \over {27{x^9}}}$$

$${1 \over {9{x^4}}}$$

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

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