$\text { Find the indefinite integral of } \int \frac { 1 } { x + 5 } d x \text {. }$
A) $- \ln | x + 5 | + C$
B) $\frac { 1 } { x + 5 } + C$
C) $\frac { 1 } { ( x + 5 ) ^ { 2 } } + C$
D) $\frac { 1 } { x ^ { 2 } + 5 } + C$
E) $\ln | x + 5 | + C$

Question

$\text { Find the indefinite integral of } \int \frac { 1 } { x + 5 } d x \text {. }$ 
A) $- \ln | x + 5 | + C$
B) $\frac { 1 } { x + 5 } + C$
C) $\frac { 1 } { ( x + 5 ) ^ { 2 } } + C$
D) $\frac { 1 } { x ^ { 2 } + 5 } + C$
E) $\ln | x + 5 | + C$

Quizplus · Accepted Answer

This is a basic integration problem using the formula for the natural logarithm. Recall that the indefinite integral of $\frac{1}{x}$ is $\ln|x|+C$. In this case, we have $\frac{1}{x+5}$, which is of the form $\frac{1}{x-a}$ where $a=-5$. Therefore, using a substitution of $u=x+5$, we can rewrite the integral as $\int\frac{1}{u}\,du=\ln|u|+C=\ln|x+5|+C$. Hence the answer is $\boxed{	ext{(E)}}$.

Find the indefinite integral of ∫1x+5dx. \text { Find the indefinite integral of } \int \frac { 1 } { x + 5 } d x \text {. } Find the indefinite integral of ∫x+51​dx.

$\text { Find the indefinite integral of } \int \frac { 1 } { x + 5 } d x \text {. }$