Search results:
83.
$\int \dfrac{\cos^2 x}{\sin x}dx=\ln\left|\tan\dfrac{x}{2}\right|+cosx+C$
85.
$\int \dfrac{dx}{\sin^2x \cos x} = - \dfrac{1}{\sin x}+\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{2}\right)\right|+C$
86.
$\int \dfrac{dx}{\sin x \cos^2x}=\dfrac{1}{\cos c}+\ln\left|\tan\frac{x}{2}\right|+C$
88.
$\int \sin mx \sin nx dx = -\dfrac{\sin(m+n)x}{2(m+n)}+\dfrac{\sin(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
89.
$\int \cos mx \cos nx dx = \dfrac{\sin(m+n)x}{2(m+n)}+\dfrac{\sin(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
92.
Integral of arcsin
$\int \arcsin x dx = x\arcsin x + \sqrt{1-x^2}+C$
93.
$\int \sin mx \cos nx dx = -\dfrac{\cos(m+n)x}{2(m+n)}-\dfrac{\cos(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
94.
Integral of arccos
$\int \arccos x dx = x\arccos x-\sqrt{1-x^2}+C$
95.
Integral of arctan
$\int \arctan x dx = x\arctan x - \dfrac{1}{2}\ln\left(x^2+1\right)+C$