# integration of 1/x

• Apr 19th 2014, 12:44 AM
delso
integration of 1/x
can i change the above expression to the below expression? why?

• Apr 19th 2014, 12:58 AM
delso
Re: integration of 1/x
here's my question actually https://www.flickr.com/photos/123101...3/13933620504/

here's the working, second photo is continuous from the first
https://www.flickr.com/photos/123101...3/13910042102/
https://www.flickr.com/photos/123101...3/13933180755/

if i cant do it in such way, can you please show me how do u get the ans please? thanks in advance!
• Apr 19th 2014, 07:50 AM
delso
Re: integration of 1/x
anybody can help plaese?
• Apr 19th 2014, 08:52 AM
romsek
Re: integration of 1/x
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.
• Apr 19th 2014, 08:59 AM
JeffM
Re: integration of 1/x
Delso

• Apr 19th 2014, 09:45 AM
Shakarri
Re: integration of 1/x
$\int 1+ \frac{6}{6-x} dx$

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

$\int 1 dx + \int \frac{6}{6-x} dx$

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

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

Changing the fraction doesn't really help with solving it though, try the change of variable y=6-x
• May 10th 2015, 03:16 PM
TheVirtualMathematician
Re: integration of 1/x