Question

The value of $\int \frac{e^{6\log x}-e^{5\log x}}{e^{4\log x}-e^{3\log x}}dx$ is equal to

• A. $0$
• B. $\frac{x^3}{3}$
• C. $\frac{3}{x^3}$
• D. $\frac{1}{x}$

Answer 1

The correct option is B $\frac{x^3}{3}$

$\int \frac{e^{6\log x}-e^{5\log x}}{e^{4\log x}-e^{3\log x}}dx$
$=\int \frac{x^6-x^5}{x^4-x^3}dx$
$=\int x^2\frac{x^4-x^3}{x^4-x^3}dx$
$=\int x^{2}dx$
$=\frac{x^3}{3}$