Applications of Integration - Integration as an Inverse Process of Differentiation

Show that \(\frac{\mathrm{d}}{\mathrm{d}x}(\tan^{3}x) = 3\sec^{4}x - 3\sec^{2}x\).

Hence find \(\displaystyle\displaystyle \displaystyle\int \sec^{4}x\) \(dx\).