Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Various Forms and Results of Integrals

Voice

Voice

Home

Integration using Identities

when f(x) = Pi_(i=1)^n g_i(x), use identities to convert to f(x) = sum_(i=1)^m h_i(x), such that integration can be individually performed on h_i(x).

### Integration using Identities

plain and simple summary

nub

plain and simple summary

nub

dummy

When the integrand is product of several functions, convert that to sum of functions using known identities.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.

In this page, integration using identities is explained with examples.

Keep tapping on the content to continue learning.
Starting on learning "". In this page, integration using identities is explained with examples.

Consider the integration int (x+2)(x+3) dx. Which of the following would help in working out the integral?

• use an identity to convert the multiplication to a sum of terms
• a polynomial in factors form cannot be integrated

The answer is "use an identity to convert the multiplication to a sum of terms"

int (x+2)(x+3) dx.

use the identity (x+a)(x+b) = x^2+(a+b)x+ab
=int [x^2 + (2+3)x + 2xx3 ]dx

This integral can be computed for each of the terms.

Consider the integration int cos^2 x dx. Which of the following would help in working out the integral?

• use a trigonometric identity to convert cos^2 x into sum of terms
• only numerical integration is possible

The answer is "use a trigonometric identity to convert cos^2 x into sum of terms "

We know the trigonometric identity cos2x = cos^2 x - sin^2 x

substitute sin^2 x = 1-cos^2x and rearrange the terms
cos^2 x = (1+cos2x)/2

int cos^2 x dx

=int [1/2 + (cos2x)/2 ]dx

This integral can be computed for each of the terms.

Some trigonometric identities useful for integration are

2sinxcosy = sin(x+y)+sin(x-y)
2sinxcosx = sin(x+y)

2cosxcosy = cos(x-y)+cos(x+y)
2cos^2x = 1+cos(2x)
4cos^3x = 3cosx + cos3x

2sinxsiny = cos(x-y)-cos(x+y)
2sin^2x = 1-cos(2x)
sin^3x = 3sinx - sin3x

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Integration using Identities: when f(x) = Pi_(i=1)^n g_i(x) Use identities to convert to f(x) = sum_(i=1)^m h_i(x), such that integration can be individually performed on h_i(x).

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Integrate int cos^2 x dx + int sin^2 x dx.

• use the identity cos^2x + sin^2 x = 1
• cannot use the identity cos^2x + sin^2 x = 1

The answer is "use the identity cos^2x + sin^2 x = 1"

your progress details

Progress

About you

Progress

Consider the integration, integral x + 2 multiplied x + 3 d x. Which of the following would help in working out the integral.
use;identity;convert;multiplication
use an identity to convert the multiplication to a sum of terms
polynomial;factors;form;not;
a polynomial in factors form cannot be integrated
The answer is "use an identity to convert the multiplication to a sum of terms"
Integration is worked out as given.
Consider the integration: integral cos squared x dx. Which of the following would help in working out the integral.
use;trigonometric;identity;convert
use a trigonometric identity to convert cos squared x into sum of terms
only;numerical;possible
only numerical integration is possible
The answer is "use a trigonometric identity to convert cos squared x into sum of terms"
We know the trigonometric identity cos 2 x = cos squared x minus sine squared x. The integration is worked out using that.
Some trigonometric identities useful for integration are given.
Simplified nub: When the integrand is product of several functions, convert that to sum of functions using known identities.
Reference Jogger: Integration using Identities is summarized.
Integrate the given expression.
1
2
The answer is "use the identity cos squared x + sin squared x = 1"

we are not perfect yet...