Question

give the antiderivatives of $\frac{1}{x}$, for $x > 0$.
choose the correct answer below.
a. $-x + c$, where $c$ is an arbitrary constant
b. $ln x + c$, where $c$ is an arbitrary constant
c. $-x$
d. $ln x$

Explanation:

Step1: Recall antiderivative rule

The antiderivative of $\frac{1}{x}$ is $\ln|x|+C$ for $x
eq0$. Since $x > 0$, the absolute - value can be removed.

Step2: Consider constant of integration

When finding antiderivatives, we must include the arbitrary constant $C$. So the antiderivative of $\frac{1}{x}$ for $x>0$ is $\ln x + C$.

Answer:

B. $\ln x + C$, where $C$ is an arbitrary constant