∫(e^6log x-e^5log x)/(e^4log x-e^3log x)dx=

\(\int\frac{e^{6\log x}-e^{5\log x}}{e^{4\log x}-e^{3\log x}}dx=\int\frac{x^6-x^5}{x^4-x^3}dx\)

$=\int\frac{x^5(x-1)}{x^3(x-1)}dx$

$=\int x^2dx=\frac{x^3}{3}+C$