$\int \frac{5-\ln x}{x} d x=5 \ln |x|-\frac{(\ln |x|)^{2}}{2}+C$ .

Name: $\int \frac{5-\ln x}{x} d x=5 \ln |x|-\frac{(\ln |x|)^{2}}{2}+C$ .
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Question

Quizplus · Accepted Answer

The integral can be split into two parts: $\int \frac{5}{x} dx$ and $\int \frac{-\ln x}{x} dx$. The first part integrates to $5\ln|x|$, and the second part integrates to $-\frac{(\ln|x|)^2}{2}$, resulting in $5\ln|x| - \frac{(\ln|x|)^2}{2} + C$.

∫5−ln⁡xxdx=5ln⁡∣x∣−(ln⁡∣x∣)22+C\int \frac{5-\ln x}{x} d x=5 \ln |x|-\frac{(\ln |x|)^{2}}{2}+C∫x5−lnx​dx=5ln∣x∣−2(ln∣x∣)2​+C

$\int \frac{5-\ln x}{x} d x=5 \ln |x|-\frac{(\ln |x|)^{2}}{2}+C$