It is given that

\(y=(10x+2)\ln(5x+1).\)

(i) Find \(\dfrac{dy}{dx}\).

(ii) Hence show that

\(\int \ln(5x+1)\,dx=\frac{ax+b}{5}\ln(5x+1)-x+c,\)

where \(a\) and \(b\) are integers and \(c\) is a constant of integration.

(iii) Hence find

\(\int_0^{1/5}\ln(5x+1)\,dx,\)

giving your answer in the form \(\dfrac{d+\ln f}{5}\), where \(d\) and \(f\) are integers.