For x² ≠ n π + 1, n N (the set of natural numbers), the integral ∫ x√((2 sin (x² - 1) - sin 2(x² - 1))/(2 sin (x² - 1) + sin 2(x² - 1))) dx is equal to: (where c is a constant of integration)

(D) log e | sec ((x² - 1)/2) | + c

(A) log e | 1/2 sec ²(x² - 1) | + c

(B) 1/2 log e | sec (x² - 1) | + c

(C) 1/2 log e | sec ²((x² - 1)/2) | + c

Integral Calculus: JEE Main 2019 Mathematics question

JEE Main 2019 · 9 Jan, Morning shift · Q4020

JEE Main 20199 Jan, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

For x²

\ne

\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)