Answer
$e^y+\sin (xz)+c$
Work Step by Step
$f(x,y,z)=\int_0^x f_1 (t,0,0) dt+ \int_0^y f_2 (x,t,0) dt+\int_0^z f_3 (x,y,t) dt$
This implies that
$f(x,y,z)=\int_0^x (0) \cos (t \cdot 0) dt+ \int_0^y (e^t) dt+\int_0^z x \cos xt dt$
Thus,
$f(x,y,z)=[e^t]_0^y+x(1/x)[\sin t]_0^x+c=e^y+\sin (xz)+c$
