Find $5,7,9,21,23$ and $25$

Evaluate the surface integral of the scalar function.

$5.{}_{S}x+y+zdS,$ where $S$:$x=u+v,y=u-v,z=1+2u+v$ with $0u2,0v1.$

$7.{}_{S}ydS,$ where $S$:vec$(r)(u,v)=($:ucosv,usinv,$v$:$)$ with $0u1,0v.$

$9.{}_S{x}^{2}yzdS,$ where $S$ is the part of the plane $z=1+2x+3y$ that lies above the rectangle $[0,3][0,2]$

Evaluate the surface integral of the vector field.

$21.{}_S$vec$(F)*dvec(S),$ where vec$(F)(x,y,z)=($:$z{e}^{xy},-3z{e}^{xy},xy$:$)$ and $S$:$x=u+v,y=u-v,z=1+2u+v$ with $0u2,0v1$ and upward orientation.

$23.{}_S$vec$(F)*dvec(S),$ where vec$(F)(x,y,z)=($:$xy,yz,xz$:$)$ and $S$:$z=4-x^2-y^2$ with $0x1,0y1$ and upward orientation.

$25.{}_S$vec$(F)*dvec(S),$ where vec$(F)(x,y,z)=($:$x,y,z^2$:$)$ and $S$ is the unit sphere $x^2+y^2+z^2=1,$ equipped with outward pointing normal vectors. $($Hint: Use vec$(r)(,)=($:$sincos,sinsin,cos$:$)$ to parameterize $S$ and take the normal vector vec$(n)=$vec$(r{)}_{}$vec$(r{)}_{},$ which points outward,$)$