JEE Advance - Mathematics (1994 - No. 2)
Find the indefinite integral $$\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)} {\mkern 1mu} d\theta $$
$$\frac{\sin 2\theta}{2} ln\left(\frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta}\right) - \frac{1}{2} ln(\sec 2\theta) + C$$
$$\frac{\cos 2\theta}{2} ln\left(\frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta}\right) - \frac{1}{2} ln(\sec 2\theta) + C$$
$$\frac{\sin 2\theta}{2} ln\left(\frac{\cos \theta - \sin \theta}{\cos \theta + \sin \theta}\right) - \frac{1}{2} ln(\sec 2\theta) + C$$
$$\frac{\sin 2\theta}{2} ln\left(\frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta}\right) + \frac{1}{2} ln(\sec 2\theta) + C$$
$$\frac{\sin \theta}{2} ln\left(\frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta}\right) - \frac{1}{2} ln(\sec 2\theta) + C$$