# Who's up to the challenge? 64

Calculus Level 5

$\large \int _{ 0 }^{ 2\ln { \phi } }{ \ln { \left( 2\sinh { \left( \dfrac { x }{ 2 } \right) } \right) dx } } =-\dfrac { { \pi }^{ a } }{ b }$

Let $$\phi$$ denotes the Golden ratio, $$\phi = \dfrac{1+\sqrt5}2 \approx 1.618$$.

If the equation above holds true for integers $$a$$ and $$b$$, find $$a\times b$$.

×