Answer
$V=\pi\ln 2$
Work Step by Step
Using the washer method, the volume of the solid is:
$V=\int_{0}^{1}\pi(\frac{1}{\sqrt{x+1}})^{2}dx$
$V=\int_{0}^{1}\pi\frac{1}{x+1}dx$
$V=\pi\int_{0}^{1}\frac{1}{x+1}dx$
$V=\pi\int_{0}^{1}\frac{(x+1)'}{x+1}dx$
Using the fudamental theorem of calculus it follows:
$V=\pi[\ln(x+1)]_{0}^{1}$
$V=\pi(\ln(1+1)-\ln(0+1))$
$V=\pi\ln 2$