Join TSR now and get all your revision questions answeredSign up now
 You are Here: Home >< Maths

# Basic standard integral Watch

1. Basically we have been given a sheet with all the standard integrals we should know.

I don't however understand this one:

Integral f'(g(x))g'(x)dx = f(g(x)) + c

Would someone using latex just give an example using a simple equation as then I should see it much clearer!

Thanks
2. (Original post by TimothyTankT)
Basically we have been given a sheet with all the standard integrals we should know.

I don't however understand this one:

Integral f'(g(x))g'(x)dx = f(g(x)) + c

Would someone using latex just give an example using a simple equation as then I should see it much clearer!

Thanks
Use a substitution of and it should drop out. That integrand is in the form of the derivative of a composite function.
3. (Original post by TimothyTankT)
Basically we have been given a sheet with all the standard integrals we should know.

I don't however understand this one:

Integral f'(g(x))g'(x)dx = f(g(x)) + c

Would someone using latex just give an example using a simple equation as then I should see it much clearer!

Thanks
It is the rule for the integration of compodite functions and the base of this notation
is the definition of undetermined integral namely
so that

from this

If function f in composite, for example f(g(x)), then from the chain rule
where f' is derivative of outer function
substituting g(x) in x multiplied by the derivative of inner function, g'(x).
So integrating this

Generally
where H is the primitive function of h.
For example:

because the primitive function of 1/x is ln|x| and the derivative of cosx is -sinx.
F.e 2.

4. Try differentiating f(g(x)). Use a substitution u = g(x).

Write a reply… Reply
Submit reply
Updated: October 28, 2010
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### HELP!

Mum wants to come to Freshers with me

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.