Biết có (intlimits_2^4 {dfrac{1}{{2x + 1}},dx = mln 5 + nln 3,left( {m,n in R} right)} ). Tính P = m – n .

Ta có:

(intlimits_2^4 dfrac{1}{{2x + 1}},dx )

(= dfrac{1}{2}intlimits_2^4 dfrac{1}{{2x + 1}},dleft( {2x + 1} right) )

(= dfrac{1}{2}ln left| {2x + 1} right|left| begin{array}{l}{}^4\_2end{array} right. )

(= ln 3 – dfrac{1}{2}ln 5 = mln 5 + nln 3, )

Khi đó ta có: (left{ begin{array}{l}n = 1\m =  – dfrac{1}{2}end{array} right. Rightarrow P = m – n =  – dfrac{3}{2}.)

Chọn đáp án A.