Too large for graphing

Using $\large{\displaystyle \int^{\infty}_{0} \frac{1}{1+x^{n}}dx=\frac{\pi}{n}\csc \left(\frac{\pi}{n}\right) \qquad (1)}$ ,

This has been proved a lot of times on brilliant. Hint put $y=1/(1+x^n)$ and beta function.

Now in $(1)$ put $x=\frac{t}{a}$ , thus we have

$\large{\displaystyle \int^{\infty}_{0} \frac{1}{1+\frac{t^{n}}{a^n}}dt=a \frac{\pi}{n}\csc \left(\frac{\pi}{n}\right)}$

The given integral is

$\large{\displaystyle \int^{\infty}_{0} \frac{1}{1+\frac{x^{2016}}{2016}}dx}$

Here $\large{a=2016^{\frac{1}{2016}};n=2016}$

The final answer is

$\Large{\frac{\pi}{2016^{\frac{2015}{2016}}}\csc \left(\frac{\pi}{2016}\right)}$