Definite integrals for common trigonometric functions > $\huge \begin{align} \int \sin (x) \d{x} &= - \cos x + C \\ \int \cos (x)\d{x} &= \sin x + C \\ \int \sec^2(x) \d{x} &= \tan x + C \\ \int \tan(x) \d{x} &= \ln \left|\sec (x) \right| + C \\ \\ \int \frac{1}{\sqrt{1-x^2}} \d{x} &= \sin^{-1} + C \\ \int \frac{1}{1+x^2} \d{x} &= \tan^{-1} + C \\ \end{align} $