Answer
$xe^{y+2z}+C$
Work Step by Step
Here, $f=xe^{y+2z}+g(y,z)$
and $g(y,z)=0$ or, $g(y,z)=h(z)=0$
Then $f=xe^{y+2z}+h(z)$
This implies that
$f_z=2xe^{y+2z}+h'(z)=2xe^{y+2z}$
Hence, $f=xe^{y+2z}+C$
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