(a) Integrate the following with respect to \(x\).
(i) \(\mathrm{e}^{5 x-2}\)
(ii) \(\frac{1}{4-3 x}\) where \(x\lt \frac{4}{3}\)
(b) Show that \(\int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \sec ^{2}\left(\frac{1}{2} x\right) \mathrm{d} x=2\left(1-\frac{\sqrt{3}}{3}\right)\).