$\int \sin x ~  dx = -\cos x + C \\$ $\int \cos x ~ dx = \sin x + C \\$ $\int \sin^2x ~ dx= \dfrac{x}{2}-\dfrac{1}{4} ~ \sin(2x) + C \\$ $\int \cos^2x ~ dx = \dfrac{x}{2}+\dfrac{1}{4} ~ \sin(2x) + C \\$ $\int \sin^3x ~ dx = \dfrac{1}{3}~ \cos^3x-\cos x + C \\$ $\int \cos^3x ~ dx = \sin x - \dfrac{1}{3}~ \sin^3x + C \\$ $\int \dfrac{dx}{\sin x} = \ln\left| \tan \dfrac{x}{2} \right| + C \\$ $\int \dfrac{dx}{\cos x} = \ln\left| \tan \left(\dfrac{x}{2} + \dfrac{\pi}{4}\right)\right| + C \\$ $\int \dfrac{dx}{\sin^2x} = -\cot x + C \\$ $\int \dfrac{dx}{\cos^2x} = \tan x + C \\$ $\int \dfrac{dx}{\sin^3x} = -\dfrac{\cos x}{2\cdot \sin^2x} + \dfrac{1}{2}~ \ln \left|\tan\dfrac{x}{2}\right| + C \\$ $\int \dfrac{dx}{\cos^3x} = \dfrac{\sin x}{2\cdot \cos^2x} + \dfrac{1}{2} ~ \ln\left|\tan\left(\dfrac{x}{2}+\dfrac{\pi}{2}\right)\right| + C \\$ $\int \sin x \cdot \cos x dx = - \dfrac{1}{4}~\cos(2x) + C \\$ $\int \sin^2x \cdot \cos x dx = \dfrac{1}{3}~ \sin^3x + C\\$ $\int \sin x \cdot \cos^2x dx = -\dfrac{1}{3}~ \cos^3x + C\\$ $\int \sin^2x \cdot \cos^2x dx = \dfrac{x}{8}-\dfrac{1}{32}~ \sin(4x) + C\\$ $\int \tan x~dx = -\ln|\cos x| + C \\$ $\int \dfrac{\sin x}{\cos^2x}~ dx = \dfrac{1}{\cos x} + C\\$ $\int \dfrac{\sin^2x}{\cos x}~ dx = \ln \left|  \tan\left( \dfrac{x}{2}+\dfrac{\pi}{4}\right ) \right| - \sin x + C \\$ $\int \tan^2x~dx = \tan x-x   + C\\$ $\int \cot x~dx =\ln|\sin x| + C \\$ $\int \dfrac{\cos x}{\sin^2x}dx=-\dfrac{1}{\sin x} + C \\$ $\int \dfrac{\cos^2x}{\sin x}~ dx = \ln\left|\tan\dfrac{x}{2}\right| + \cos x + C \\$ $\int \cot^2x~dx = -\cot x - x + C \\$ $\int \dfrac{dx}{\sin x \cdot \cos x} = \ln|\tan\,x| + C \\$ $\int \dfrac{dx}{\sin^2x \cdot \cos x} = -\dfrac{1}{\sin x} + \ln\left|\tan\left(\dfrac{x}{2} + \dfrac{\pi} {4}\right)\right| + C \\$ $\int \dfrac{dx}{\sin x \cdot \cos^2x}=\dfrac{1}{\cos x}+\ln\left|\tan\dfrac{x}{2}\right| + C \\$ $\int \dfrac{dx}{\sin^2x \cdot \cos^2x}=\tan x - \cot x + C \\$ $\int \sin(mx)\cdot \sin(nx)~dx = -\dfrac{\sin(m+n)x}{2(m+n)} + \dfrac{\sin(m-n)x}{2(m-n)}+ C , \quad m^2 \ne n^2 \\$ $\int \sin(mx)\cdot \cos(nx)~dx = -\dfrac{\cos(m+n)x}{2(m+n)} - \dfrac{\cos(m-n)x}{2(m-n)}+ C , \quad m^2 \ne n^2 \\$ $\int \cos(mx)\cdot \cos(nx)~dx = \dfrac{\sin(m+n)x}{2(m+n)} + \dfrac{\sin(m-n)x}{2(m-n)}+ C , \quad m^2 \ne n^2 \\$ $\int \sin x \cdot \cos^nx~dx = \dfrac{\sin^{n+1}x}{n+1} + C \\$ $\int \sin^nx \cdot \cos\,x~dx = \dfrac{\sin^{n+1}x}{n+1} + C \\$ $\int \sin^{-1}x~dx = x\cdot \sin^{-1} x + \sqrt{1-x^2} + C \\$ $\int \cos^{-1} x~dx = x \cdot \cos^{-1} x - \sqrt{1-x^2} + C \\$ $\int \tan^{-1} x ~dx = x \cdot \tan^{-1} x - \dfrac{1}{2}~\ln(1+x^2) + C \\$ $\int \mathrm{cot^{-1}}\,x~dx = x \cdot \mathrm{cot^{-1}}\,x + \dfrac{1}{2}~\ln(1+x^2) + C\\$

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