Вычислите интеграл \(\large{{{\int\limits_{0}^1}{\frac{2^x+3^x}{6^x}}\,dx}}\) . \(\large{\frac{2}{3\ln3}+\frac{1}{2\ln2}}\) \(\large{\frac{1}{3}+\frac{1}{\ln2}}\) \(\dfrac{5}{6}\) \(\large\frac{\ln2\ln3}{\ln6}\)

Задание

Вычислите интеграл \(\large{{{\int\limits_{0}^1}{\frac{2^x+3^x}{6^x}}\,dx}}\) .

\(\large{\frac{2}{3\ln3}+\frac{1}{2\ln2}}\)
\(\large{\frac{1}{3}+\frac{1}{\ln2}}\)
\(\dfrac{5}{6}\)
\(\large\frac{\ln2\ln3}{\ln6}\)