$\int \frac{\ln (7+x)}{7+x} d x=(\ln (7+x))^{2}+C$ .

Question

Quizplus · Accepted Answer

The correct integral of $\frac{\ln(7+x)}{7+x}$ with respect to $x$ is $\ln|7+x|\ln|C(7+x)|$, where $C$ is the constant of integration. The given equation mistakenly applies a rule for integrating powers of functions, which is not applicable in this case. The correct method involves recognizing the integral as a form that can be solved using integration by parts or recognizing it directly if familiar with the integral of $\frac{\ln(x)}{x}$.

∫ln⁡(7+x)7+xdx=(ln⁡(7+x))2+C\int \frac{\ln (7+x)}{7+x} d x=(\ln (7+x))^{2}+C∫7+xln(7+x)​dx=(ln(7+x))2+C

$\int \frac{\ln (7+x)}{7+x} d x=(\ln (7+x))^{2}+C$