(a)

(i) Find

\(\int\frac1{(10x-1)^6}\,dx.\)

(ii) Find

\(\int\frac{(2x^3+5)^2}{x}\,dx.\)

(b)

(i) Differentiate \(y=\tan(3x+1)\) with respect to \(x\).

(ii) Hence find

\(\int_{\pi/12}^{\pi/10}\left(\frac{\operatorname{sec}^2(3x+1)}2-\sin x\right)\,dx.\)