=∫6xdx=6xlog6+c=6xlog(2*3)+c=6xlog2+log3+c=2x.3xlog2+log3+c

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$\int 2^{x} 3^{x} d x =$

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$2^{x} 3^{x} + c$

$2^{x} \log 2 + 3^{x} \log 2 + c$

$\frac{2^{x}}{\log 2} + \frac{3^{x}}{\log 2} + c$

$\frac{2^{x} 3^{x}}{\log 2 + \log 3} + c$

answer is D.

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Detailed Solution

$= \int 6^{x} d x$

$= \frac{6^{x}}{\log 6} + c$

$= \frac{6^{x}}{\log (2 * 3)} + c$

$= \frac{6^{x}}{\log 2 + \log 3} + c$

$= \frac{2^{x} {.3}^{x}}{\log 2 + \log 3} + c$

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