Integration formulas

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


For properties of definite integration go through the following link
Properties of definite integration

For complete list of class 12 Maths important formulas go through the following link
Class 12 Maths Important Formula

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