${\int }_0^4\{\frac{x}{4}\}(1+\left[\tan \left(\frac{\left\{x\right\}}{1+\left\{x\right\}}\right)\right])dx=\left(\text{The greatest integer function is denoted by }\left[\text{x}\right]\right)$

$\text{where as the fractional part function is denoted by }\left\{\text{x}\right\}.$