Integration formulas for exponential functions
\int x^n \, dx = \frac{1}{n+1}x^{n+1} + C For n≠−1
\int e^x \, dx = e^x + C
\int a^x \, dx = \frac{a^x}{\ln(a)} + C For a≠1
\int \frac{1}{x} \, dx = \ln|x| + C
Integration formulas for Trigonometric Functions
\int \sin(x) \, dx = -\cos(x) + C
\int \cos(x) \, dx = \sin(x) + C
\int \tan(x) \, dx = \ln|\sec(x)| + C
\int \csc(x) \, dx = -\ln|\csc(x) + \cot(x)| + C
\int \sec(x) \, dx = \ln|\sec(x) + \tan(x)| + C
\int \cot(x) \, dx = \ln|\sin(x)| + C
\int \frac{1}{\sqrt{1 - x^2}} \, dx = \sin^{-1}(x) + C
\int \frac{1}{\sqrt{1 - x^2}} \, dx = -\cos^{-1}(x) + C
\int \frac{1}{1 + x^2} \, dx = \tan^{-1}(x) + C
\int \frac{1}{1 + x^2} \, dx = -\cot^{-1}(x) + C
\int \frac{1}{x\sqrt{x^2 - 1}} \, dx = \sec^{-1}(x) + C
\int \frac{1}{x\sqrt{x^2 - 1}} \, dx = -\cosec^{-1}(x) + C
Integral formulas for some special functions.
\int \frac{1}{x^2 - a^2} \, dx = \frac{1}{2a}\ln\left|\frac{x - a}{x + a}\right| + C
\int \frac{1}{a^2 - x^2} \, dx = \frac{1}{2a}\ln\left|\frac{a + x}{a - x}\right| + C
\int \frac{1}{x^2 + a^2} \, dx = \frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right) + C
\int \frac{1}{\sqrt{x^2 - a^2}} \, dx = \ln\left|x + \sqrt{x^2 - a^2}\right| + C
\int \frac{1}{\sqrt{a^2 - x^2}} \, dx = \sin^{-1}\left(\frac{x}{a}\right) + C
\int \frac{1}{\sqrt{x^2 + a^2}} \, dx = \ln\left|x + \sqrt{x^2 + a^2}\right| + C
\int \sqrt{x^2 + a^2} \, dx = \frac{x}{2}\sqrt{x^2 + a^2} + \frac{a^2}{2}\ln\left|x + \sqrt{x^2 + a^2}\right| + C
\int \sqrt{x^2 - a^2} \, dx = \frac{x}{2}\sqrt{x^2 - a^2} - \frac{a^2}{2}\ln\left|x + \sqrt{x^2 - a^2}\right| + C
\int \sqrt{a^2 - x^2} \, dx = \frac{a^2}{2}\sin^{-1}\left(\frac{x}{a}\right) + \frac{x}{2}\sqrt{a^2 - x^2} + C
