# Evaluating $\int_0^\pi \frac{x}{(\sin x)^{\sin (\cos x)}}\,\mathrm{d}x$

Evaluate $$\int_0^\pi \frac{x}{(\sin x)^{\sin (\cos x)}}\,\mathrm{d}x.$$

I tried using by parts and complex numbers along with series expansion but I was unable to find the answer.
• Just for hee-haws, it turns out that $$\frac{\cos{x}}{(\sin{x})^{\sin{\cos{x}}}}$$ has an antiderivative in closed form. – Ron Gordon Nov 21 '14 at 11:47
• The one equals $$3.9905179137710221001990755970868667785510732535206.$$ – user64494 Nov 21 '14 at 12:40