Question

Integrate: dy/(1-y^2)

Anybody knows how to integrate this without the weird Arctanh(x) ?

Answer 1

\[\int\limits \frac{dy}{ (1-y^2)}\]
Let \[y= sinx \rightarrow dy = cosx dx\]
Thus
\[\int\limits \frac{dy}{ (1-y^2)} = \int\limits \frac{cosx dx}{ (1-\sin^2x)}= \int\limits \frac{cosx dx}{ (\cos^2x)}\]
\[= \int\limits \frac{ dx}{ (cosx)} = \int\limits \sec x dx = \log|\sec x + \tan x| +c\]