Question

Hyperbolic trig functions mabob

Answer 1

So here's an example \[\int\limits \frac{dx}{1+x^2}\]

Answer 2

\[x=\sinh t \\ dx = \cosh t dt\]

Answer 3

@Jhannybean pretend there was actually a square root

\[\int\limits \frac{\cosh t dt }{ \sqrt{1+\sinh^2 t}} = \int\limits \frac{\cosh t dt }{ \sqrt{\cosh^2 t}}\]

Answer 4

So the original one is\[\int\limits \frac{dx}{ \sqrt{1+x^2}}\]

Answer 5

so here's like an example where you could use hyperbolic trig sub I guess. The rest is obvious I think.

Answer 6

so we can add this to our trig substitution rules