Formulas
1. Standard Integrals \(\displaystyle \int x^n\,dx=\frac{x^{n+1}}{n+1}+C,\qquad n\ne -1\) \(\displaystyle \int \frac{1}{x}\,dx=\ln|x|+C\) \(\displaystyle \int (ax+b)^n\,dx=\frac{(ax+b)^{n+1}}{a(n+1)}+C,\qquad n\ne -1\) \(\displaystyle \int e^x\,dx=e^x+C\) \(\displaystyle \int a^x\,dx=\frac{a^x}{\ln a}+C,\qquad a>0,\ a\ne1\) \(\displaystyle \int \sin x\,dx=-\cos x+C\) \(\displaystyle \int \cos x\,dx=\sin x+C\) \(\displaystyle \int \tan x\,dx=-\ln|\cos x|+C\) \(\displaystyle \int \cot x\,dx=\ln|\sin x|+C\) \(\displaystyle \int \sec^2x\,dx=\tan x+C\) \(\displaystyle \int \csc^2x\,dx=-\cot x+C\) \(\displaystyle \int \sec x\tan x\,dx=\sec x+C\) \(\displaystyle \int \csc x\cot x\,dx=-\csc x+C\) \(\displaystyle \int \sec x\,dx=\ln|\sec x+\tan x|+C\) \(\displaystyle \int \csc x\,dx=\ln|\csc x-\cot x|+C\) \(\displaystyle \int \sin(ax)\,dx=-\frac1a\cos(ax)+C\) \(\displaystyle \int \cos(ax)\,dx=\frac1a\sin(ax)+C\) \(\displaystyle \int \tan(ax)\,dx=-\frac1a\ln|\cos...