# Antiderivative Formula

## Antiderivative Formula

An antiderivative is anything that is the inverse of a function and has been differentiated in trigonometric terms. The Antiderivative Formula and differentiated functions are both continuous on a given interval. A differentiable function F whose derivative is identical to the original function f is referred to as an antiderivative, primitive function, primitive integral, or indefinite integral of a function f in calculus.

The Antiderivative Formula rules in mathematics are fundamental principles for determining the antiderivatives of various function combinations. Antidifferentiation, as the name implies, is the opposite of differentiating. These Antiderivative Formula assist us in determining the antiderivative of a function’s sum or difference, product and quotient, scalar multiple of a function and constant function, and function composition. The Antiderivative Formula rules assist us in making the process of locating antiderivatives more straightforward.

The following is a list of the most often used Antiderivative Formula rules for the product, quotient, sum, difference, and composition of functions:

Antiderivative Power Rule

Antiderivative Chain Rule

Antiderivative Product Rule

Antiderivative Quotient Rule

Antiderivative Rule for Scalar Multiple of Function

Antiderivative Rule for Sum and Difference of Functions

### Basic Antiderivatives

In this part, they will go through the formulae for the various antiderivative laws covered previously in depth. They will go through the principles for antidifferentiation of algebraic functions with power, as well as other function combinations. The Antiderivative Formula laws are frequent for functions such as trigonometric, exponential, logarithmic, and algebraic functions.

### Antiderivative Rules

The Antiderivative Formula rules are some of the most significant principles for determining the antiderivatives of various sorts of function combinations. These antiderivative rules may be used to find the antiderivatives of functions such as product, quotient, sum, difference, scalar multiple, and composition of functions. These laws apply to algebraic functions, exponential functions, trigonometric functions, hyperbolic functions, logarithmic functions, and constant functions.

### Important Antiderivative Rules Notes

The antiderivatives principles are used to calculate the antiderivatives of various algebraic, trigonometric, logarithmic, exponential, inverse trigonometric, and hyperbolic function combinations.

Most differentiation rules have matching antiderivative rules for antidifferentiation.

The Antiderivative Formula rule for a constant function f(x) = k is ∫k dx = kx + C

### Trigonometric Function Antiderivative Rules

Trigonometric functions are divided into six categories: sine, cosine, tangent, cotangent, secant, and cosecant. They will now investigate the Antiderivative Formula  of these trigonometric functions as follows:

∫sin x dx = -cos x + C

∫cos x dx = sin x + C

∫tan x dx = ln |sec x| + C

∫cot x dx = ln |sin x| + C

∫sec x dx = ln |sec x + tan x| + C

∫csc x dx = ln |cosec x – cot x| + C