Answer
$\pi(24\ln{4} -\frac{27}{4})$
Work Step by Step
Setup the integration using washer method about the line y=4
$\pi \int_0^3 [(4)^2 - (4-\frac{3}{1+x})^2]dx$
$\pi \int_0^3(16-(16-\frac{24}{1+x}+\frac{9}{(1+x)^2}))dx$
$\pi \int_0^3(\frac{24}{1+x}- \frac{9}{(1+x)^2})dx$
$\pi \int_0^3 (24u^{-1} - 9u^{-2})du$, use u substitution to integrate
$\pi [ 24\ln{u} +\frac{9}{u}]_1^4$ , use change of variables and evaluate the definite integral
$\pi((24\ln{4} +\frac{9}{4})-(24\ln{1} +9))$
$\pi(24\ln{4} -\frac{27}{4})$
