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# Methods of Integration

Examples showing how various functions can be integrated View other versions (4)

## Introduction

The following methods of Integration cover all the Normal Requirements of A.P.; A. level; The International Baccalaureate as well as Engineering Degree Courses.

It does not cover approximate methods such as The Trapezoidal Rule or Simpson's Rule. These will be covered in another paper.

## Simple Algebraic Equations

Except when n = -1 Then

## Rational Algebraic Functions Whose Denominator Factorizes

Here is a worked example

## Rational Algebraic Functions Whose Denominators Do Not Factorize

Here are some examples

Example:
Problem
Workings
Solution

Example:
Problem
Workings
Solution
Other forms

## An Irrational Function Of The Following Type

thus the original equation can now be rewritten as :-

Example:
##### Example -
Problem

Find the integral of

Workings
let U =

The integral can now be written as :-
Solution

## An Irrational Function Containing

substitute
So the integral is now rational in
Example:
##### Example -
Problem
Find the integral of
Workings
Substitute
i.e.

Therefore

### Todo

Review the following workings

thus the integral can be written as:-
Solution
Therefore

## Using Trigonometrical Formula

Example:
##### Example -
Problem

To find the integral of

Workings
But
from which it can be shown that
Solution

### Any Trigonometrical Formula

To integrate any trigonometrical function such as

Example:
Problem
Workings
Solution
Therefore

Then
Example:
Problem
Workings
Solution

Example:
Problem
Workings
Solution

## Integration By Parts

this can also be written as:-
Example:
Problem
Workings
Solution

Example:
Problem

Workings

Solution
Therefore