Find the integral.
-$\int \frac{d x}{(5+\ln x) x}$
A) $\ln |5+\ln x|+C$
B) $\ln (5+\ln x)+C$
C) $5 \ln |5+\ln x|+C$
D) $\frac{1}{5} \ln |5+\ln x|+C$

Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = 5 + \ln x $, then $ du = \frac{1}{x} dx $. The integral becomes $\int \frac{1}{u} du$, which is $\ln |u| + C$. Substituting back, we get $\ln |5+\ln x| + C$.

Find the Integral ∫dx(5+ln⁡x)x\int \frac{d x}{(5+\ln x) x}∫(5+lnx)xdx​ A) ln⁡∣5+ln⁡x∣+C\ln |5+\ln x|+Cln∣5+lnx∣+C

Find the Integral $\int \frac{d x}{(5+\ln x) x}$ A) $\ln |5+\ln x|+C$