evaluate the following indefinite integral. ∫(11 + u)/u du ∫(11 + u)/u du = (use parentheses to clearly…

Answer:

$11\ln|u| + u + C$

Explanation:

Step1: Split the fraction

$\int\frac{11 + u}{u}du=\int(\frac{11}{u}+\frac{u}{u})du=\int(\frac{11}{u}+ 1)du$

Step2: Integrate term - by - term

$\int(\frac{11}{u}+ 1)du=\int\frac{11}{u}du+\int 1du$

Step3: Apply integration rules

$\int\frac{11}{u}du = 11\int\frac{1}{u}du=11\ln|u|$ and $\int 1du = u$ So, $\int\frac{11 + u}{u}du=11\ln|u|+u + C$ (where $C$ is the constant of integration)