反応速度
∫ 0 x d x ( [ A ] 0 − x ) ( [ B ] 0 − x ) = 1 [ B ] 0 − [ A ] 0 ( ln  1 [ A ] 0 − x − ln  1 [ B ] 0 − x ) − 1 [ B ] 0 − [ A ] 0 ( ln  [ B ] 0 − ln  [ A ] 0 ) = 1 [ B ] 0 − [ A ] 0 ( ln  [ A ] 0 [ A ] 0 − x − ln  [ B ] 0 [ B ] 0 − x ) {\displaystyle {\begin{aligned}&\int _{0}^{x}{\frac {\mathrm {d} x}{([\mathrm {A} ]_{0}-x)([\mathrm {B} ]_{0}-x)}}\\&={\frac {1}{[\mathrm {B} ]_{0}-[\mathrm {A} ]_{0}}}\left(\ln {\frac {1}{[\mathrm {A} ]_{0}-x}}-\ln {\frac {1}{[\mathrm {B} ]_{0}-x}}\right)-{\frac {1}{[\mathrm {B} ]_{0}-[\mathrm {A} ]_{0}}}(\ln[\mathrm {B} ]_{0}-\ln[\mathrm {A} ]_{0})\\&={\frac {1}{[\mathrm {B} ]_{0}-[\mathrm {A} ]_{0}}}\left(\ln {\frac {[\mathrm {A} ]_{0}}{[\mathrm {A} ]_{0}-x}}-\ln {\frac {[\mathrm {B} ]_{0}}{[\mathrm {B} ]_{0}-x}}\right)\end{aligned}}}