Answer
$\frac{6(56 \log 4 - 10\log7)}{(\log7)(\log 4)}$
Work Step by Step
$\int(7^x-4^x)dx$
$=\frac{7^x}{\log 7}-{4^x}{\log 4}+C$ (indefinite integral)
$\int(7^x-4^x)dx$ $|_1^3$
$=(\frac{7^3}{\log7}-\frac{4^3}{\log4})-(\frac{7}{\log7}-\frac{4}{\log4})$
$=\frac{6(56 \log 4 - 10\log7)}{(\log7)(\log 4)}$
