question 4 · 1 point evaluate the indefinite integral given below. provide your answer below…
question 4 · 1 point evaluate the indefinite integral given below. provide your answer below: (int\frac{8}{5x}dx=)
Answer
Explanation:
Step1: Use integral rule
Recall that $\int\frac{a}{x}dx=a\ln|x| + C$ (where $a$ is a constant). Here $a = \frac{8}{5}$. So, $\int\frac{8}{5x}dx=\frac{8}{5}\int\frac{1}{x}dx$.
Step2: Evaluate integral
Since $\int\frac{1}{x}dx=\ln|x|+C$, then $\frac{8}{5}\int\frac{1}{x}dx=\frac{8}{5}\ln|x|+C$.
Answer:
$\frac{8}{5}\ln|x|+C$