basic integration help needed

• Jan 8th 2010, 07:04 AM
Dergyll
basic integration help needed
Hello guys, just finish learning about Derivatives and Limits yesterday, so I thought I could get started on Integration now.

I've looked in alot of places but can't find out how to integrade a multiplication/division! I mean, addition and subtraction are easy stuff, just distribute the integral sign but how are multiplication, division handled?

Here:
Integrate: 3x(Cos(x^3 + 7))
Integrate: (x+1)/(x-1)

Thanks for any help!
Derg
• Jan 8th 2010, 07:18 AM
Sudharaka
Dear Dergyll,

In the first integration have you written,$\displaystyle \int{3xCos(x^3+7)dx}\mbox{ or }\int{3Cos(x^3+7)dx}$ Please confirm this and then I will try to help.
• Jan 8th 2010, 07:44 AM
Dergyll

your first integration is correct, its a 3 "x" not multiplication.
• Jan 8th 2010, 07:54 AM
Sudharaka
Dear Dergyll

2)$\displaystyle \int{{\frac{x+1}{x-1}}dx}=\int{\frac{x-1+2}{x-1}}dx=\int{dx}+2ln\mid{x-1}\mid+C=x+2ln\mid{x-1}\mid+C$

I shall try to do your first sum when time permits. But for the moment the answer escapes me.
• Jan 8th 2010, 08:45 AM
Shanks
$\displaystyle \int{3xCos(x^3+7)dx}$ cann't be expressed as elementary function, see Wolfram.
• Jan 8th 2010, 10:39 AM
Dergyll
Ok, but how do I use the integration by parts method? Why if the problem occurs something like this?

$\displaystyle \int (2x^3+5x+1) (e^2x) dx$
• Jan 8th 2010, 10:58 AM
tom@ballooncalculus
Just in case a picture helps...

http://www.ballooncalculus.org/asy/parts/e.png

... bigger...

... where

http://www.ballooncalculus.org/asy/prod.png

... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. And integration by parts is a matter of filling out this rule usefully but starting (unlike in differentiation) with one of the lower corners instead of at the top. So the basic pattern is...

http://www.ballooncalculus.org/asy/maps/parts.png

... and choosing legs crossed or uncrossed is equivalent to asigning u, v, and du and dv

By the way, other brands of IBP are available. E.g. tabular. And of course this is 'integration by parts thrice', because we have to repeat the pattern until the order of the polynomial goes to zero.

And I take it this is a new example you're asking about - if you wanted to tackle the 3x(Cos(x^3 + 7)) by parts then, no, no deal. Can't be expressed as elementary means can't be done, basically (roughly).

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• Jan 8th 2010, 11:14 AM
TWiX
Quote:

Originally Posted by Dergyll
Integrate: (x+1)/(x-1)
Derg

Try u = x-1
then (x+1)/(x-1) = ? (in terms of u)
dx = ?