I have this indefinite integral problem.. How am I supposed to go about questions like this?

integral of ln(x)

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- Nov 14th 2008, 05:13 AMdankelly07indefinite integration
I have this indefinite integral problem.. How am I supposed to go about questions like this?

integral of ln(x) - Nov 14th 2008, 06:07 AMMath_Helper
Attachment 8691

(Hi)(Talking) - Nov 15th 2008, 07:44 AMqpmathelp
use integration by parts with 1 as the second function

that is make it ln(x) *1

try the following page for more explanation

mixture: integral of ln(x) using integration by parts - Nov 15th 2008, 08:21 AMMathstud28
I always suggest to people that for problems like this if it is not apparently obvious why not try a substitution? Let $\displaystyle \ln(x)=z\Rightarrow{x=e^z}\implies{dx=e^zdz}$. Then $\displaystyle \int\ln(x)dx\overbrace{\mapsto}^{z=\ln(x)}\int{ze^ zdz}$. Now it should be apparent what method to use.

- Nov 15th 2008, 09:52 AMtom@ballooncalculus
Don't integrate - balloontegrate!

Drawing the product rule thus...

http://www.ballooncalculus.org/mhf8.gif

or thus...

http://www.ballooncalculus.org/mhf9.gif

... (in which the straight lines differentiate, downwards, with respect to x) the challenge of integration by parts is to fill out the shape usefully but starting (unlike in differentiation) in one of the lower balloons...

http://www.ballooncalculus.org/mhf10.gif

As with u and v, some trial and error (or intelligent forethought, or L.I.A.T.E) may be necessary - but possibly less confusing having the picture with which to find one's way. Anyway, the right road is...

http://www.ballooncalculus.org/mhf11.gif

... in which the only problem is that the lower level is no longer equal to what we wanted to integrate. So correct that...

http://www.ballooncalculus.org/mhf12.gif

... and complete the integration ...

http://www.ballooncalculus.org/mhf13.gif

Balloon Calculus: worked examples from past papers - Nov 19th 2008, 03:05 AMdankelly07
Thanks guys all useful posts..

balloontegrating looks nuts, but it def helps..