give the antiderivatives of $\frac{1}{x}$, for $x > 0$.\nchoose the correct answer below.\na. $-x + c$…

give the antiderivatives of $\frac{1}{x}$, for $x > 0$.\nchoose the correct answer below.\na. $-x + c$, where $c$ is an arbitrary constant\nb. $ln x + c$, where $c$ is an arbitrary constant\nc. $-x$\nd. $ln x$

give the antiderivatives of $\frac{1}{x}$, for $x > 0$.\nchoose the correct answer below.\na. $-x + c$, where $c$ is an arbitrary constant\nb. $ln x + c$, where $c$ is an arbitrary constant\nc. $-x$\nd. $ln x$

Answer

Explanation:

Step1: Recall antiderivative rule

The antiderivative of $\frac{1}{x}$ is $\ln|x|+C$ for $x\neq0$. 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