Chapter 5.4, Problem 208E

In the following exercises, evaluate the triple integrals over the bounded region $E=\left\{\left(x,y,z\right)|\left(x,y\right)\in D,u_1\left(x,y\right)x\le z\le u_2\left(x,y\right)\right\},$ where D is the projection of E onto the xy —plane.

208. ${\displaystyle \underset{D}{\iint }\left({\displaystyle \underset{1}{\overset{3}{\int }}x\left(z+1\right)dz}\right)dA,}$ where $D=\left\{\left(x,y\right)|x^2-y^2\ge 1,x\le \sqrt{5}\right\}$