Cho tích phân sau (I = intlimits_3^5 {frac{1}{{2x – 1}}dx} = aln 3 + bln 5,,,left( {a,b in mathbb{Q}} right)). Tính (S = a + b.)

(begin{array}{l}I = intlimits_3^5 {frac{1}{{2x – 1}}dx}  = left. {frac{1}{2}ln left| {2x – 1} right|} right|_3^5\,,,, = frac{1}{2}left( {ln left| {2.5 – 1} right| – ln left| {2.3 – 1} right|} right)\,,,, = frac{1}{2}.left( {ln 9 – ln 5} right) = ln 3 – frac{1}{2}ln 5\ Rightarrow a = 1;,,b =  – frac{1}{2}.end{array})

Vậy (S = a + b = 1 – frac{1}{2} = frac{1}{2}.)

Chọn D.