# What is the net area between f(x) = 1/sqrt(x^2+2x+1)  and the x-axis over x in [2, 4 ]?

$\sqrt{{x}^{2} + 2 x + 1} = \left\mid 1 + x \right\mid$ so $f \left(x\right) = \frac{1}{\left\mid 1 + x \right\mid}$ the area is the ${\int}_{2}^{4} f \left(x\right) \mathrm{dx} = \ln \left(1 + x\right) {|}_{2}^{4} = \ln \left(5\right) - \ln \left(3\right) = \ln \left(\frac{5}{3}\right)$