Question

What happens when you can't integrate a function for a certain value of x? For example, the integration of ln(x) equals xln(x)-x +C where x is a negative number. I was thinking if ln(x) is a first order, then the integration should be a horizontal line, but that does not seem to make much sense because taking the derivative should give you a line. I'm confused!!

Answer 1

no the integral of ln(x) should be absolute value xln(x) - x + C

Answer 2

But how do I calculate it without my calculator or Excel telling me that it doesn't work; put in absolute value signs around the whole thing, or just x?

Answer 3

just around (x). Because you can't take the natural log of a (-x) to begin with, which means the integral of a ln(-x) will never exist.

So if you are asked to integrate ln(x), it has to be absolute value of (x). So you're integral should really be ln(absolute value (x))

Answer 4

Thank-you!