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Indefinite Integrals question

2019 · 9 Jan · Shift 1 · Q39

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PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2019 · 9 Jan · Shift 1 · Q39

Indefinite Integrals question

2019 · 9 Jan · Shift 1 · Q39

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

For x2

e

n

\pi

+ 1, n

\in

N (the set of natural numbers), the integral

\int {x\sqrt {{{2\sin ({x^2} - 1) - \sin 2({x^2} - 1)} \over {2\sin ({x^2} - 1) + \sin 2({x^2} - 1)}}} dx}

is equal to : (where c is a constant of integration)

A
${\log _e}\left| {{1 \over 2}{{\sec }^2}\left( {{x^2} - 1} \right)} \right| + c$
B
${1 \over 2}{\log _e}\left| {\sec \left( {{x^2} - 1} \right)} \right| + c$
C
${1 \over 2}{\log _e}\left| {{{\sec }^2}\left( {{{{x^2} - 1} \over 2}} \right)} \right| + c$
D
${\log _e}\left| {\sec \left( {{{{x^2} - 1} \over 2}} \right)} \right| + c$

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