$$ \int \tan x dx=-ln|cosx|+C $$
$$ \int \cot x dx= ln|sinx|+C $$
$$ \int sec x dx = ln|sec x + tanx|+C $$
$$ \int csc x dx = ln|cscx-cotx|+C $$
$$ \int sec^2xdx=tanx+C $$
$$ \int csc^2xdx=-cotx+C $$
$$ \int secxtanxdx=sec x +C $$
$$ \int cscx cotx dx=-cscx+C $$
$$ \int \frac{1}{a^2+x^2}dx=\frac{1}{a}arctan \frac{x}{a}+C \quad(a>0) $$
$$ \int \frac{1}{a^2-x^2}dx=\frac{1}{2a}ln|\frac{x+a}{x-a}|+C $$
$$ \int \frac{1}{\sqrt[]{a^2-x^2} }dx=arcsin \frac{x}{a}+C \quad (a>0) $$
$$ \int \frac{1}{\sqrt[]{x^2+a^2}}=ln(x+\sqrt[]{x^2+a^2})+C $$
$$ \int \frac{1}{\sqrt[]{x^2-a^2}}=ln|x+\sqrt[]{x^2-a^2}|+C $$
$$ \int \sqrt{a^2-x^2}dx=\frac{a^2}{2}arcsin \frac{x}{a}+\frac{x}{2}\sqrt[]{a^2-x^2}+C \quad (a>|x|\ge0) $$
$$ \int sin^2xdx=\frac{x}{2}-\frac{sin2x}{4}+C $$
$$ \int cos^2xdx=\frac{x}{2}+\frac{sin2x}{4}+C $$
$$ \int tan^2xdx=tanx-x+C $$
$$ \int cot^2xdx=-cotx-x+C $$
$$ \int e^u[\frac{1}{u+1}-\frac{1}{(u+1)^2}]du = \frac{e^u}{u+1} + C $$