Use the Log Rule to find the indefinite integral for $\int \frac { 1 } { 4 - 6 x } d x$ .
A) $- \frac { 1 } { 6 } \ln | 4 + 6 x | + C$
B) $\frac { 1 } { 4 } \ln | 4 - 6 x | + C$
C) $- \frac { 1 } { 6 } \ln | 4 - 6 x | + C$
D) $\frac { 1 } { 4 } \ln | 4 + 6 x | + C$
E) $\frac { 1 } { 6 } \ln | 4 - 6 x | + C$

Question

Quizplus · Accepted Answer

The integral $\int \frac { 1 } { 4 - 6 x } d x$ can be solved by recognizing it as a form suitable for direct application of the logarithmic integration rule. To make it more apparent, factor out the coefficient of $x$ from the denominator: $\int \frac { 1 } { -6(6x - 4) } d x$. This leads to $-\frac{1}{6} \ln |4 - 6x| + C$, which matches option C.

Use the Log Rule to Find the Indefinite Integral For \int