Question

Describe methods of Integration.

Answer 1

Hint:In order to describe the methods of integration, we should first know that integration is. An integration is called anti-derivative for a given derivative function. It is represented by the $\int {dx} $ sign. It is a method of adding values on a large scale. There are different types of integration methods that are used to find an integral of some function.

Complete answer:
The different methods used in integration are:
-Integration by Substitution
-Integration by Parts
-Integration using Trigonometric Identities
-Integration of Some Particular function
-Integration by partial function

Further describing the methods listed above:
Integration by Substitution: Sometimes, it is difficult to solve the integration of a function simply, so we add another variable or, replace some larger function with a new variable.
Integration by Parts: Integration by parts is a special integration of a function, where a given function is a multiple of two or more functions. It is represented by the formula: $\int {f(x)g'(x)dx = f(x)g(x) - \int {f'(x)g(x)dx} } $.

Integration using Trigonometric Identities:In this type of integration, where trigonometric values/identities are used. A given function that can be an identity for some function, which is expanded then integrated.
Integration of Some particular function: In this function it involves some important formula of integration that can be applied to make other integration into the standard form of the integrand, then simply integrating the function using the direct method of integration.
Integration by partial fraction: A rational function that can be defined as the ratio of two polynomials which can be expressed in the form of partial fractions; Basically, there are two forms of partial fraction, proper partial fraction and improper partial fraction.

Note:Different methods of integration give’s different outputs/results for the given function sometimes. The ILATE rule is used to decide which term should be differentiated first and integrated first. The term which is closer to L is differentiated first and the term closer to E is integrated first in integration methods.