Question

The value of the integral $\int \frac{e^{7\log x}-e^{6\log x}}{e^{5\log x}-e^{4\log x}}dx$ is equal to

• A. $e^7\cdot \log 7+c$
• B. $\frac{x^3}{3}+c$
• C. $e\cdot 5^{5x}+c$
• D. $\frac{e^2}{\log 2}+c$

Answer 1

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

$\int \frac{e^{7\log x}-e^{6\log x}}{e^{5\log x}-e^{4\log x}}dx=\int \frac{x^7-x^6}{x^5-x^4}dx=\int x^{2}dx=\frac{x^3}{3}+c$