current objective evaluate indefinite integrals involving exponential or logarithmic functions question…
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:
$\frac{1}{2}\ln|x|+C$