Integration Formulas

About Integration Formulas

Integral Formulas — Integration is the inverse of differentiation, also known as Inverse Differentiation. The process of finding a function's derivative is known as integration. Here are some basic integration formulas for various functions. Apart from the basic integration formulas, this article also includes a taxonomy of integral formulas, as well as a few, practise questions based on the integration formulas discussed. Integrating the product of two functions, such as y = uv, is referred to as integration by parts.

• $\int dx = x + C$
• $\int x^{n}dx = \frac{x^{n+1}}{n+1} + C$
• $\int \frac{dx}{x}=\ln \left|x\right|+C$
• $\int e^{x}dx = e^x+C$
• $\int a^{x}dx = \frac{1}{\ln a}{a}^{x }+C$
• $\int \ln x dx= x \ln x - x + C$
• $\int \sin x dx =-\cos x + C$
• $\int \cos x dx =\sin x + C$
• $\int \tan x dx =-\ln |\cos x| + C$
• $\int cot x dx = \ln |\sin x| + C$
• $\int sec x dx = \ln |sec x + \tan x| + C$
• $\int csc x dx = - \ln |csc x + cot x| + C$
• $\int se{c}^2 x dx = \tan x+C$
• $\int cs{c}^2 x dx = - cot x+C$
• $\int sec x \tan x dx = sec x + C$
• $\int csc x cot x dx = - csc x + C$
• $\int \frac{dx}{\sqrt{a^2- x^2}} = {\sin }^{-1}\frac{x}{a}+C$
• $\int \frac{dx}{a^2+x^2}=\frac{1}{a }{\tan }^{-1}\frac{x}{a}+C$
• $\int \frac{dx}{x\sqrt{x^2 - a^2}}= \frac{1}{a}se{c}^{-1}\frac{\left|x\right|}{a}+C$

Classification of Integral Formulas

The integral formulas described above are categorized using the functions below.

1. Rational functions
2. Irrational functions
3. Trigonometric functions
4. Inverse trigonometric functions
5. Hyperbolic functions
6. Inverse hyperbolic functions
7. Exponential functions
8. Logarithmic functions
9. Gaussian functions

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