integration of 1/x

romsek

MHF Helper
Nov 2013
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3,032
California
The first part is pretty straightforward

$y=Vx$

$\dfrac {dy}{dx}=V+x\dfrac {dV}{dx}$

just substitute those into your original equation and simplify.

Then the diff eq in V is separable so separate it and solve.
 
Feb 2014
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Delso

For next time, it does not help to respond to your own initial post. That means your thread disappears from the list of unanswered posts and may greatly delay your getting an answer.
 
Oct 2012
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Ireland
\(\displaystyle \int 1+ \frac{6}{6-x} dx\)

Well you are right that integration can be separated when two expressions are added or subtracted, integration has this additive property. The equation would become

\(\displaystyle \int 1 dx + \int \frac{6}{6-x} dx\)

But you made a little mistake with your fraction, the fraction can be changed to

\(\displaystyle \int 1 dx + \int \frac{3}{\frac{1}{2}(6-x)} dx\)

Changing the fraction doesn't really help with solving it though, try the change of variable y=6-x