Question

Integrate:$\int \frac{dt}{6t-1}$

• A. $\frac{1}{6}ln(6t-1)+C$
• B. $\frac{1}{12}ln(6t-1)+C$
• C. $\frac{1}{6}ln(12t-1)+C$
• D. $\frac{6}{1}ln(6t-1)+C$

Answer 1

The correct option is A $\frac{1}{6}ln(6t-1)+C$

Assume,
$u=6t–1$
$\frac{du}{dt}=6\Rightarrow \frac{du}{6}=dt$
$I=\int \frac{dt}{6t-1}=\frac{1}{6}\int \frac{du}{u}$
$=\frac{1}{6}ln|u|+C$
$=\frac{1}{6}ln(6t-1)+C$