# Tricky Integration

• Feb 8th 2009, 04:57 AM
hairymclairy
Tricky Integration
Could anyone help me integrate the following equation;

e^(x+y) + ln(x) + (e^(x+y) + y^2)dy/dx = 0

I can see it is exact and in the form P(x,y) + Q(x,y)dy/dx=0 and so I should be able to solve it using the partial differentiation method, but that would mean integrating ln x with respect to x, which I thought was impossible.

Many thanks.
• Feb 8th 2009, 05:01 AM
skeeter
Quote:

Originally Posted by hairymclairy
... but that would mean integrating ln x with respect to x, which I thought was impossible.

$\displaystyle \int \ln{x} \, dx = x(\ln{x} - 1) + C$
• Feb 8th 2009, 05:05 AM
hairymclairy
Thanks, I've never seen that result before. Which is slightly disconcerting.
• Feb 8th 2009, 05:07 AM
Moo
Quote:

Originally Posted by hairymclairy
Thanks, I've never seen that result before. Which is slightly disconcerting.

You can easily get this result by an integration by parts :

$\displaystyle \int \ln(x) ~dx$
u=ln(x)
dv=1