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| + CIntegration 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) + CIntegral 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