Integration is a fundamental concept in calculus, and it involves finding the antiderivative of a function. An antiderivative is a function whose derivative is equal to the given function. Integration formulae are the backbone of this process and provide a structured way to solve integrals. The basic integration formula list includes formulas for simple functions such as constants, powers, exponentials, logarithms, trigonometric functions, and inverse trigonometric functions.

The use of integration formulae allows for the evaluation of complex integrals and helps to simplify mathematical calculations. The integration formula list serves as a comprehensive guide for students and professionals alike. By memorizing these formulas and understanding their applications, individuals can quickly and accurately evaluate integrals.

## All Integration Formula List

The below list of integral formulas that may be encountered while solving integration problems.

### List of Basic Integration Formulas

- ∫ 1 dx = x + C
- ∫ a dx = ax+ C
- ∫ x
^{n }dx = ((x^{n+1})/(n+1))+C ; n≠1 - ∫ sin x dx = – cos x + C
- ∫ cos x dx = sin x + C
- ∫ sec
^{2}x dx = tan x + C - ∫ csc
^{2}x dx = -cot x + C - ∫ sec x (tan x) dx = sec x + C
- ∫ csc x ( cot x) dx = – csc x + C
- ∫ (1/x) dx = ln |x| + C
- ∫ e
^{x }dx = e^{x}+ C - ∫ a
^{x }dx = (a^{x}/ln a) + C ; a>0, a≠1

### List of Integration Formulas of Trigonometric

The below list of integration formulas of trigonometric and inverse trigonometric functions.

- ∫ cos x dx = sin x + C
- ∫ sin x dx = -cos x + C
- ∫ sec
^{2}x dx = tan x + C - ∫ cosec
^{2}x dx = -cot x + C - ∫ sec x tan x dx = sec x + C
- ∫ cosec x cot x dx = -cosec x + C
- ∫ tan x dx = log |sec x| + C
- ∫ cot x dx = log |sin x| + C
- ∫ sec x dx = log |sec x + tan x| + C
- ∫ cosec x dx = log |cosec x – cot x| + C

### List of Integration Formulas of Inverse Trigonometric

These are the integral formulas that result in the form of inverse trigonometric functions.

- ∫1/√(1 – x
^{2}) dx = sin^{-1}x + C - ∫ 1/√(1 – x
^{2}) dx = -cos^{-1}x + C - ∫1/(1 + x
^{2}) dx = tan^{-1}x + C - ∫ 1/(1 + x
^{2}) dx = -cot^{-1}x + C - ∫ 1/x√(x
^{2}– 1) dx = sec^{-1}x + C - ∫ 1/x√(x
^{2}– 1) dx = -cosec^{-1}x + C

### Advanced Integration Formulas List

The below list of advanced integral formulas that one may encounter while solving integration problems.

- ∫1/(x
^{2}– a^{2}) dx = 1/2a log|(x – a)(x + a| + C - ∫ 1/(a
^{2}– x^{2}) dx =1/2a log|(a + x)(a – x)| + C - ∫1/(x
^{2}+ a^{2}) dx = 1/a tan^{-1}x/a + C - ∫1/√(x
^{2}– a^{2})dx = log |x +√(x^{2}– a^{2})| + C - ∫ √(x
^{2}– a^{2}) dx = x/2 √(x^{2}– a^{2}) -a^{2}/2 log |x + √(x^{2}– a^{2})| + C - ∫1/√(a
^{2}– x^{2}) dx = sin^{-1 }x/a + C - ∫√(a
^{2}– x^{2}) dx = x/2 √(a^{2}– x^{2}) dx + a^{2}/2 sin^{-1}x/a + C - ∫1/√(x
^{2}+ a^{2 }) dx = log |x + √(x^{2}+ a^{2})| + C - ∫ √(x
^{2}+ a^{2 }) dx = x/2 √(x^{2}+ a^{2 })+ a^{2}/2 log |x + √(x^{2}+ a^{2})| + C

### List of Integration Formula PDF With Examples

Download pdf list of all integration formulas with examples from below link.

https://people.math.sc.edu/josephcf/Teaching/142/Files/Lecture%20Notes/Chapter8/8.pdf