current objective evaluate indefinite integra...

current objective evaluate indefinite integrals involving exponential or logarithmic functions question evaluate the indefinite integral given below. ∫ 1/2x dx provide your answer below: ∫ 1/2x dx = □

Answer

# Explanation: ## Step1: Factor out the constant We know that $\int\frac{1}{2x}dx=\frac{1}{2}\int\frac{1}{x}dx$ since $\int kf(x)dx = k\int f(x)dx$ where $k=\frac{1}{2}$ and $f(x)=\frac{1}{x}$. ## Step2: Use the integral formula The integral of $\frac{1}{x}$ is $\ln|x|+C$. So, $\frac{1}{2}\int\frac{1}{x}dx=\frac{1}{2}\ln|x| + C$. # Answer: $\frac{1}{2}\ln|x|+C$