Annual Integral!

$\begin{aligned} I & = \int_{2016}^{2017} \left(x^{\frac {2016}{2015}}-2016x^{\frac 1{2015}}\right)^{2015} dx \\ & = \int_{2016}^{2017} x(x-2016)^{2015} dx & \small \color{#3D99F6} \text{Let }u=x-2016 \implies du = dx \\ & = \int_0^1 (u+2016)u^{2015} du \\ & = \int_0^1 \left(u^{2016}+2016u^{2015}\right) du \\ & = \frac 1{2017} + 1 = \boxed{\dfrac {2018}{2017}} \end{aligned}$

$\displaystyle\int_{2016}^{2017} \left( x^{\frac{2016}{2015}}- 2016 x^{\frac{1}{2015}} \right)^{2015}dx$

$\displaystyle=\int_{2016}^{2017}\left( (x-2016)x^{\frac1{2015}} \right)^{2015} dx$

$\displaystyle=\int_{2016}^{2017} (x-2016)^{2015}x dx$

$\displaystyle=\int_0^1 u^{2015}(u+2016) du$ ( $x=u+2016,dx=du$ )

$\displaystyle=\int_0^1 u^{2016}+2016u^{2015}du$

$\displaystyle=\frac1{2017}+1=\frac{2018}{2017}$