(a) Show that

\(\frac{1}{2x+1}-\frac{1}{(2x+1)^2}+\frac{4}{4x-1} =\frac{24x^2+14x+4}{(2x+1)^2(4x-1)}.\)

(b) Hence find

\(\int_{\frac12}^{1}\frac{24x^2+14x+4}{(2x+1)^2(4x-1)}\,dx,\)

giving your answer in the form \(\frac12\ln p+q\), where \(p\) and \(q\) are rational numbers.