 #1
Alettix
 177
 11
Homework Statement
Calculate the integral:
## \int_{a}^{b} \frac{1}{x} dx ##
Homework Equations

The Attempt at a Solution
In high school we learned that:
## \int_{a}^{b} \frac{1}{x} dx = ln(x) + C ##
because the logarithm of a negative number is undefined.
However, in my current maths course about complex numbers we leared to take the logarithms of negative numbers as well, using: ##ln(x) = ln(x) + \pi i ##. With this extension, can we say:
## \int_{a}^{b} \frac{1}{x} dx = ln(x) + C ##
or is this still wrong?
Thank you very much!