List of top Mathematics Questions on Definite and indefinite integrals asked in AP EAPCET

Evaluate \[ \int \frac{2\cos x+1}{(2+\cos x)^2}\,dx-\frac{\sin x}{2+\cos x} \]

If \[ \int \frac{1}{\cos 4x \cos 2x}\,dx = \frac{1}{4\sqrt{2}}\log\left|\frac{1+f(x)}{1-f(x)}\right| -\frac{1}{2}\log g(x)+C, \] then \[ g\left(\frac{\pi}{6}\right)-\sqrt{2}f\left(\frac{\pi}{6}\right)= \]