Help with this Trigonometry integral I've to find this integral:
$$\int_{\frac{\pi}{365}}^{\frac{365} {\pi}}\left(\frac{4^\pi}{\tan(x)}+\tanh^{-1}(x)-4\sec^2(x)\right)dx$$
So far as I know to go:
$$\int_{\frac{\pi}{365}}^{\frac{365} {\pi}}\left(\frac{4^\pi}{\tan(x)}+\tanh^{-1}(x)-4\sec^2(x)\right)dx=$$
$$\int_{\frac{\pi}{365}}^{\frac{365} {\pi}}\left(4^\pi\cdot \frac{1}{\tan(x)}+\tanh^{-1}(x)-4\sec^2(x)\right)dx=$$
$$\int_{\frac{\pi}{365}}^{\frac{365} {\pi}}\left(4^\pi \cot(x)+\tanh^{-1}(x)-4\sec^2( x)\right)dx$$
Thanks a lot!

The hyperbolic tangent is between $-1$ and $1$, so the inverse hyperbolic tangent is not defined outside that range.  At least, it's not real.
