Integration rules and how to calculate it

Integration and differentiation are two basic principle operations in calculus. Integration rules are the same as differentiation. As you already have known the differentiation and integration are the inverse of one other but keep this thing in mind when we integrate a function, the answer will always contain a constant of unknown value, called constant of integration, C.

Integration rules
Below are some important and basic rules which we use for integrating most types of the functions
 The power rule
 The constant-coefficient rule
 The sum rule
 The difference

The power rule

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The power rule of the integration is basically applied to find the indefinite integral of a function and is exactly opposite to the power rule of differentiation. It provides you with a variable of the indefinite integral raised to a power.

∫ ax n dx = a x n+1 + C
n+1

Most of the time, power rule to find the indefinite integral of a function can solve your problems but not always.

The constant-coefficient rule

The constant-coefficient rule also called constant multiplier rule gives you the indefinite Integral of c.f(x), where f(x) is a particular function and c is coefficient constant and can be written as

∫ c ƒ(x) dx = c ∫ ƒ(x) dx

The sum rule

The sum rule tells you to integrate several functions that can be the sum of numerous terms. In sum rule, we integrate every term in the sum separately then add results together. The order in which the results appear is not that important.
∫ (ƒ(x) + g(x)) dx = ∫ ƒ(x) dx + ∫ g(x) dx

The difference rule

The difference rule aids you to integrate those functions that involve the difference between two or more terms. It works the same as the sum rule of the integration, the only difference is that the order of the results is important and cannot be changed.

∫ (ƒ(x) - g(x)) d = ∫ ƒ(x) dx - ∫ g(x) dx

Integral calculator to solve integration rules

To calculate all these integration rules, integral calculators can be used. Online integral calculators can be used in computing the complex integral functions in seconds. You just need to put the integral function into the input field to get results.