Question

Answer the following question

Answer 1

$\int \frac{ {e}^{5 log_{e}x } - {e}^{4 log_{e}x } }{ {e}^{3 log_{e}x } - {e}^{2 log_{e}x } } dx\\ = \int \frac{ {e}^{log_{e}( {x}^{5} ) } - {e}^{log_{e} ( {x}^{4} )} }{ {e}^{ log_{e}( {x}^{3} ) } - {e}^{ log_{e}( {x}^{2} ) } } dx \\ = \int \frac{ {x}^{5} - {x}^{4} }{ {x}^{3} - {x}^{2} } dx \\ = \int \frac{ {x}^{2} ({x}^{3} - {x}^{2} )}{ {x}^{3} - {x}^{2} } dx \\ = \int {x}^{2} dx = \frac{ {x}^{3} }{3} + c$