Question

Evaluate : 

\[\int\frac{e^{6 \log_e x} - e^{5 \log_e x}}{e^{4 \log_e x} - e^{3 \log_e x}}dx\]

Answer 1

\[\int\left( \frac{e^{6 \log x} - e^{5 \ log x}}{e^{4 \ log x} - e^{3 \ log x}} \right)dx\]

`=∫( ( e^(log x^ 6) - e^(log x^5 ))/(e^(log x^4 )-e^(log x^3)))dx` 
\[ = \int\left( \frac{x^6 - x^5}{x^4 - x^3} \right)dx\]
\[ = \int\frac{x^5}{x^3}dx\]
\[ = \int x^2 dx\]
\[ = \frac{x^3}{3} + C\]