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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int \large\frac{2^x+3^x}{6^x}$$dx$

\[\begin {array} {1 1} (a)\;\frac{-(1/3)^x}{\log 3}+\frac{(1/2)^x}{\log 2}+c \\ (b)\;\frac{(1/3)^x}{\log 3}+\frac{(1/2)^x}{\log 2}+c \\ (c)\;\frac{-(1/3)^x}{\log 3}-\frac{(1/2)^x}{\log 2}+c \\ (d)\;None \end {array}\]

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A)
$\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
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