# How to find the indefinite Integral of ln|sec|?

As per my understanding integral of $\frac{u'}{u}$ is $\ln|u|$

I tried doing that for evaluating the indefinite integral $\ln|sec(x)|$ So I got:

$$\int \ln|sec(x)| \, dx = \frac{sec(x) \tan(x)}{ sec(x) } = \tan(x)$$

But that wasn't the right answer.

1. So what would be the right answer and the logic behind it ?
2. How I would find the integral of $\ln|\sin(x)|$ or $\ln|csc(x)|$ ?
• Try integration by parts – Sak Feb 29 '16 at 4:56
• The integral of $f'/f$ equals $\ln |f|$, not the other way around. – Mattos Feb 29 '16 at 4:59
• According to W|A, there are no closed forms, but your function can be written in terms of polylogarithms. – Henricus V. Feb 29 '16 at 5:03
• You just differentiated it. – Nikunj Feb 29 '16 at 10:28