Question

Improper integrals

Answer 1

\[\int\limits_{0}^{1}\ln( e x)\]

Answer 2

I am not sure why you would use improper integrals when one of the domain is a constant

Answer 3

you should memorize the anti derivative of \(\ln(x)\) because it is very common. otherwise you have to do a rather simple integration by parts, but the anti derivative is
\[x\ln(x)-x\] in your case you have to adjust for the constant

Answer 4

oh it is improper because the log is not defined at 0
it goes to minus infinity there

Answer 5

btw don't forget that
\[\ln(ex)=\ln(e)+\ln(x)=1+\ln(x)\]

Answer 6

so you have
\[\int_0^1dx+\int_0^1\ln(x)dx=1+\int_0^1\ln(x)dx\]

Answer 7

So the answer is 1?

Answer 8

0

Answer 9

@satelite73 Why did you use integration by parts?