INDEFINITE INTEGRATION_JEE-Main-2019_090119_S1 - Competishun – Live JEE & NEET Courses and Exam Prep

JEE Main 2019

9-01-2019 S1

Question

For $x^2 \neq n \pi+1, n \in N$ (the set of natural numbers), the integral $\int x \sqrt{\frac{2 \sin \left(x^2-1\right)-\sin 2\left(x^2-1\right)}{2 \sin \left(x^2-1\right)+\sin 2\left(x^2-1\right)}} d x$ is equal to : (where c is a constant of integration)

Select the correct option:

$\frac{1}{2} \log _e\left|\sec \left(x^2-1\right)\right|+c$

$\frac{1}{2} \log _{\mathrm{e}}\left|\sec ^2\left(\frac{\mathrm{x}^2-1}{2}\right)\right|+\mathrm{c}$

$\log _{\mathrm{e}}\left|\sec \left(\frac{\mathrm{x}^2-1}{2}\right)\right|+\mathrm{c}$

$\log _e\left|\frac{1}{2} \sec ^2\left(x^2-1\right)\right|+c$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution