(a) Find \(\displaystyle\int \sqrt[3]{2x-1}\,dx\).

(b)(i) Find \(\displaystyle\int \sin4x\,dx\).

(b)(ii) Hence evaluate \(\displaystyle\int_{\pi/8}^{\pi/4}\sin4x\,dx\).

(c) Show that \(\displaystyle\int_0^{\ln8} e^{x/3}\,dx=3\).