Math Is Fun Forum

amberzak

Member

Registered: 2012-03-16

Posts: 80

Calculus - Intergration by Substitution

Hi

I can't figure this one out.

Let U = lnx

Do I tried to differentiate lnx by du. I got du=1/x dx. Then I know I need dx by itself, but not sure how to get to that.

Can anyone help me?

Thanks all

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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Calculus - Intergration by Substitution

Hi amberzak

When you use a substitution u=f(x) you should always find the relation between du and dx. You can do that by differentiating both sides using the differential operator. For this one you should get du=1/x dx. Next you write dx in terms of du i.e. dx=x*du. Now just put this instead of dx in the integral,switch the ln(x) for u and you're on your way.

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“Here lies the reader who will never open this book. He is forever dead.
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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Calculus - Intergration by Substitution

hi amberzak,

I thought 'integration by parts' might do this.

You have to choose a suitable U and dV/dx.

So I chose:

Then

So you get the same integral back!

Collect all these to the left hand side, divide by 3, and it's done.

Substitution works too.

The principle is

So you need to find dx/du

So your integral becomes

and the xs nicely cancel out to leave an easy integral.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

eterry

Member

Registered: 2012-06-16

Posts: 4

Re: Calculus - Intergration by Substitution

The substitution u=lnx will do the trick!  Then du=(1/x)dx and your integral reduces to u^2 du.

I wish there was some way to use actual math symbols.  I see everyone else using them but I don't see the option here.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Calculus - Intergration by Substitution

People are using LaTeX. LaTeX is a full document preparation system, which basically means, LaTeX proper can be used to create all kinds of documents, reports, theses, pieces of homework, anything from shopping lists to entire books. Here, however, we just use a simple engine which allows us to print mathematical symbols in the forum. So, to put everything I've said more simply, to use mathematical symbols here, type:

Just like you would use

To make things bold, e.g. bold.

If you click on 'post reply' you will find a button marked 'Math' at the bottom, next to 'B', 'I', 'U', 'Img', 'Code' and 'Quote'.

There is, in the 'Help Me!' forum a link to a post called 'LaTeX a crash course' which should give you a basic idea of the commands, many of which are fairly logical. Wikibooks also has a nice LaTeX manual. But, to give you an example:

u = \ln x
du = \frac{1}{x} \; dx
u^{2} \; du

Will produce the maths that you used in your last post, e.g.:

Also, note that if you click on the picture of the maths, it will redirect you to a page giving the exact LaTeX used by the poster, so you can see how the person has done it

Last edited by Au101 (2012-06-16 01:52:35)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Calculus - Intergration by Substitution

Hi eterry;

Welcome to the forum. Also you can look here to see some examples.

http://www.mathisfunforum.com/viewtopic.php?id=4397

You can also use this online latex site:

http://latex.codecogs.com/editor.php

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.