Integrals of Trigonometric Functions
We found 37 formulas for integrals of trigonometric functions
8.
$\int \cos^3x dx = \dfrac{1}{12}\sin 3x +\dfrac{3}{4}\sin x + C$
10.
$\int \dfrac{dx}{\cos x}=\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+C$
13.
$\int \dfrac{dx}{\sin^3x} =-\dfrac{\cos x}{2 \sin^2x}+\dfrac{1}{2}\ln\left|\tan\dfrac{x}{2}\right|+C$
14.
$\int \dfrac{dx}{\cos^3x}=\dfrac{\sin x}{2 \cos^2x}+\dfrac{1}{2}\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+C$
21.
$\int \dfrac{\sin^2x}{\cos x}dx=\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|-\sin x +C$
25.
$\int \dfrac{\cos^2 x}{\sin x}dx=\ln\left|\tan\dfrac{x}{2}\right|+cosx+C$
27.
$\int \dfrac{dx}{\sin^2x \cos x} = - \dfrac{1}{\sin x}+\ln\left|\tan\left(\frac{x}{2}+\frac{\pi}{2}\right)\right|+C$
28.
$\int \dfrac{dx}{\sin x \cos^2x}=\dfrac{1}{\cos c}+\ln\left|\tan\frac{x}{2}\right|+C$
30.
$\int \sin mx \sin nx dx = -\dfrac{\sin(m+n)x}{2(m+n)}+\dfrac{\sin(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
31.
$\int \sin mx \cos nx dx = -\dfrac{\cos(m+n)x}{2(m+n)}-\dfrac{\cos(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
32.
$\int \cos mx \cos nx dx = \dfrac{\sin(m+n)x}{2(m+n)}+\dfrac{\sin(m-n)x}{2(m-n)} + C, m^2 \ne n^2$
35.
Integral of arcsin
$\int \arcsin x dx = x\arcsin x + \sqrt{1-x^2}+C$
36.
Integral of arccos
$\int \arccos x dx = x\arccos x-\sqrt{1-x^2}+C$
37.
Integral of arctan
$\int \arctan x dx = x\arctan x - \dfrac{1}{2}\ln\left(x^2+1\right)+C$