Question

Вычеслить интеграл!!! Срочно!!!

Answer 1

$intlimits^1_{-1} {dfrac{2^{x} - 3^{x}}{6^{x}} } , dx = intlimits^1_{-1} bigg({dfrac{2^{x}}{6^{x}} - dfrac{3^{x}}{6^{x}}}bigg) , dx = intlimits^1_{-1} bigg({bigg(dfrac{1}{3}bigg)^{x} - bigg(dfrac{1}{2}bigg)^{x}bigg) =$

$= left.dfrac{bigg(dfrac{1}{3}bigg)^{x} }{ln bigg(dfrac{1}{3} bigg)} - dfrac{bigg(dfrac{1}{2}bigg)^{x} }{ln bigg(dfrac{1}{2} bigg)}}right|_{-1}^{1} = dfrac{bigg(dfrac{1}{3}bigg)^{1} }{ln bigg(dfrac{1}{3} bigg)} - dfrac{bigg(dfrac{1}{2}bigg)^{1} }{ln bigg(dfrac{1}{2} bigg)}} -left(dfrac{bigg(dfrac{1}{3}bigg)^{-1} }{ln bigg(dfrac{1}{3} bigg)} - dfrac{bigg(dfrac{1}{2}bigg)^{-1} }{ln bigg(dfrac{1}{2} bigg)}} right) =$

$= dfrac{8}{3ln(3)} - dfrac{3}{2ln (2)}$

Ответ: $dfrac{8}{3ln(3)} - dfrac{3}{2ln (2)}$

Преобразования упущены.