Question

If $\int \frac{e^{5{\log }_{e}x}-e^{4{\log }_{e}x}}{e^{3{\log }_{e}x}-e^{2{\log }_{e}x}}dx=\frac{x^3}{\lambda }+c$, then find $\lambda$

Answer 1

Answer: 3.00

$\int \frac{e^{5{\log }_{e}x}-e^{4{\log }_{e}x}}{e^{3{\log }_{e}x}-e^{2{\log }_{e}x}}dx$
$=\int \frac{x^5-x^4}{x^3-x^2}dx$
$=\int \frac{x^2\left(x^3-x^2\right)}{x^3-x^2}dx$
$=\int x^{2}dx$
$=\frac{x^3}{3}+C$