Elementary Integration Formulae

(i) $\int x^n\,dx = \dfrac{x^{n+1}}{n+1}+c,\ n\neq -1$; $\int (ax+b)^n\,dx = \dfrac{(ax+b)^{n+1}}{n+1}\cdot\dfrac1a+c$ (extends to rational $n=p/q$).\n(ii) $\int a^x\,dx = \dfrac{a^x}{\log a}+c,\ a>0$; $\int A^{ax+b}\,dx=\dfrac{A^{ax+b}}{\log A}\cdot\dfrac1a+c,\ A>0$.\n(iii) $\int e^x\,dx=e^x+c$; $\int e^{ax+b}\,dx=e^{ax+b}\cdot\dfrac1a+c$.\n(iv) $\int \cos x\,dx=\sin x+c$; $\int \cos(ax+b)\,dx=\sin(ax+b)\cdot\dfrac1a+c$.\n(v) $\int \sin x\,dx=-\cos x+c$; $\int \sin(ax+b)\,dx=-\cos(ax+b)\cdot\dfrac1a+c$.\n(vi) $\int \sec^2x\,dx=\tan x+c$; $\int \sec^2(ax+b)\,dx=\tan(ax+b)\cdot\dfrac1a+c$.\n(vii) $\int \sec x\tan x\,dx=\sec x+c$; $\int \sec(ax+b)\tan(ax+b)\,dx=\sec(ax+b)\cdot\dfrac1a+c$.\n(viii) $\int \csc x\cot x\,dx=-\csc x+c$; $\int \csc(ax+b)\cot(ax+b)\,dx=-\csc(ax+b)\cdot\dfrac1a+c$.\n(ix) $\int \csc^2x\,dx=-\cot x+c$; $ …