Determine which of the following equations is correct.
-$$x \int \frac { 1 } { 5 x } d x =$$
A) $\frac { x } { 5 } + C$
B) $\frac { x ^ { 2 } \ln | x | } { 10 } + C$
C) $\frac { x } { 5 } \ln | x | + C$
D) $5 x \ln | x | + C$

Question

Quizplus · Accepted Answer

Using the rule for integration of natural logarithmic functions, we have:
\begin{align*}
\int \frac{1}{x} \ dx &= \ln|x| + C \
\int \frac{1}{5x} \ dx &= \frac{1}{5} \ln|x| + C \
\int x \cdot \frac{1}{5x} \ dx &= \frac{x}{5} \ln|x| + C \
x \int \frac{1}{5x} \ dx &= \frac{x}{5} \ln|x| + C \
\end{align*}
Therefore, the correct choice is C.

Determine Which of the Following Equations Is Correct x∫15xdx=x \int \frac { 1 } { 5 x } d x =x∫5x1​dx=

Determine Which of the Following Equations Is Correct $x \int \frac { 1 } { 5 x } d x =$