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# Integrate : $\int \large\frac{2^x+3^x}{6^x}$$dx $\begin {array} {1 1} (a)\;\frac{-(1/3)^x}{\log 3}+\frac{(1/2)^x}{\log 2}+c \\ (b)\;\frac{(1/3)^x}{\log 3}+\frac{(1/2)^x}{\log 2}+c \\ (c)\;\frac{-(1/3)^x}{\log 3}-\frac{(1/2)^x}{\log 2}+c \\ (d)\;None \end {array}$ Can you answer this question? ## 1 Answer 0 votes \int \bigg(\large\frac{1}{3} \bigg)^x +\bigg( \large\frac{1}{2}\bigg)^x$$dx$
$\large\frac{(1/3)^x}{\log (1/3)}+\frac{(1/2)^2}{\log (1/2)}+c$
$\large\frac{-(1/3)^x}{\log 3} - \frac{(1/2)^x}{\log (2)}+c$
Hence c is the correct answer