Integration By Parts

A formula for the integral of the product of one function and the derivative of another
\[ \int f \times \frac{\mathrm{d}g}{\mathrm{d}x} \, \mathrm{d}x = \bigg[f \times g\bigg] - \int \frac{\mathrm{d}f}{\mathrm{d}x} \times g \, \mathrm{d}x \]
as shown by rearraging the terms of the product rule
\[ f \times \frac{\mathrm{d}g}{\mathrm{d}x} = \frac{\mathrm{d}(f \times g)}{\mathrm{d}x} - \frac{\mathrm{d}f}{\mathrm{d}x} \times g \]
and integrating.