Question

$\int \frac{e^{\log x}}{e^{6 \log x} - e^{5 \log x}} dx$ is equal to:

• A. $x + C$
• B. $\frac{x^2}{2} + C$
• C. $\frac{x^4}{4} + C$
• D. $\frac{x^3}{3} + C$

Hint:

For logarithmic integrals, simplify the exponentials first to make the integral more manageable.

Answer 1

The Correct Option is A

We simplify the integral as follows: \[ \frac{e^{\log x}}{e^{6 \log x} - e^{5 \log x}} = \frac{x}{x^6 - x^5} = \frac{1}{x^5(x - 1)} \] Now, using basic integration techniques, the solution to the integral is: \[ \int \frac{dx}{x^5(x - 1)} = x + C \] Thus, the answer is $x + C$.