- #1

- 685

- 4

## Homework Statement

Composing trigonometric functions, you realize that the main substitutions are related with the table below:

So, I started to integrate each expression above and I created this other table:

But I had a problem with the integral circled in red, because I don't know how transform the arctan(...) in other expression that resembles with your adjacentes functions of upper and from below.

## Homework Equations

## The Attempt at a Solution

[tex]\int \frac{\sqrt{x^2-1}}{x}dx = \sqrt{x^2-1} + \frac{i}{2} \log(x^2 - 2i \sqrt{1-x^2}-2) -i \log(x)[/tex] You have some ideia that how make the integral of ##\frac{\sqrt{x^2-1}}{x}## be similar to integrals of ##\frac{\sqrt{x^2+1}}{x}## and ##\frac{\sqrt{1-x^2}}{x}## ?