# How do you integrate f(x)=(sqrtx-1)(sqrtx+1) using the product rule?

May 26, 2018

$\frac{1}{2} {x}^{2} - x + C$
Use identity $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$
In our case $\left(\sqrt{x} - 1\right) \left(\sqrt{x} + 1\right) = x - 1$
$\int \left(x - 1\right) \mathrm{dx} = \int x \mathrm{dx} - \int \mathrm{dx} = \frac{1}{2} {x}^{2} - x + C$