Search results:
42.
$\int \dfrac{dx}{\cos x}=\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+C$
45.
$\int \dfrac{dx}{\sin^3x} =-\dfrac{\cos x}{2 \sin^2x}+\dfrac{1}{2}\ln\left|\tan\dfrac{x}{2}\right|+C$
46.
$\int \dfrac{dx}{\cos^3x}=\dfrac{\sin x}{2 \cos^2x}+\dfrac{1}{2}\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+C$
52.
$\int \dfrac{\sin^2x}{\cos x}dx=\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|-\sin x +C$
56.
$\int \dfrac{\cos^2 x}{\sin x}dx=\ln\left|\tan\dfrac{x}{2}\right|+cosx+C$
58.
$\int \dfrac{dx}{\sin^2x \cos x} = - \dfrac{1}{\sin x}+\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{2}\right)\right|+C$
59.
$\int \dfrac{dx}{\sin x \cos^2x}=\dfrac{1}{\cos c}+\ln\left|\tan\frac{x}{2}\right|+C$