Hello,(adsbygoogle = window.adsbygoogle || []).push({});

It has been over a year since I last took calculus. And I don't recall how to take the integral of a natural logarithmic function. Here is the question that I am supposed to integrate.

double integral 1/(x+y) dA

where

R = [1,2] X [0,1]

So what I did first was integrate with respect to y first. I ended up with

ln(x+y)

with an upper limit of 1 and a lower limit of 0. Once simplified I get

ln(x+1) - ln x or ln( (x+1)/x )

Now I have to integrate with respect to x. But I can't remember how to take the integral of a natural log function. How do I proceed from here?

I can't remember if I can do the following:

Let G(x) = integral of ln( (x+1)/x ) dx

then

e^G(x) = integral of e^ln( (x+1)/x ) dx

which would simplify to

integral of (x+1)/x dx.

After I get a solution to the above equation I would then take the log of

ln e^G(x) = ln (answer)

to get

G(x) = ln (answer).

Can I do that? I can't remember. If not, how do I proceed from here?

Any help is appreciated. Thankyou.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integral of a Natural Log

**Physics Forums | Science Articles, Homework Help, Discussion**