Question

$\int \frac{1}{4{\cos }^{3}x-3\cos x}dx=\frac{1}{k}\log (\sec 3x+\tan 3x).$ Find the value of $k$

Answer 1

$I=\int \frac{1}{4{\cos }^{3}x-3\cos x}dx=\int \frac{1}{\cos 3x}dx$ $=\int \sec 3xdx=\frac{1}{3}\log (\sec 3x+\tan 3x).$