Question
Integrate the function $\int {\frac{{{e^{5\log x}} - {e^{4\log x}}}}{{{e^{3\log x}} - {e^{2\log x}}}}} dx$
$ = \int {\frac{{{e^{\log {x^5}}} - {e^{\log {x^4}}}}}{{{e^{\log {x^3}}} - {e^{\log {x^2}}}}}} dx$
$=\int {\left( {\frac{{{x^5} - {x^4}}}{{{x^3} - {x^2}}}} \right)} dx$ $\left[ {\because {e^{\log \theta }} = \theta } \right]$
$ = \int {\frac{{{x^4}(x - 1)}}{{{x^2}(x - 1)}}} dx$
$ = \int {{x^2}dx} $
$ = \frac{{{x^3}}}{3} + c$
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