Answer
$\int_0^3\frac{dx}{5x+1}=\frac{4}{5}ln2$
Work Step by Step
Evaluate the integral $\int_0^3\frac{dx}{5x+1}$.
$\int_0^3\frac{dx}{5x+1}=ln[\frac{5x+1}{5}]_0^3$
$=\frac{1}{5}[ln16-ln1]$
$=\frac{1}{5}[ln 2^{4}-ln1]$
Since $ln 1= 0$
Thus, $=\frac{1}{5}[ln 2^{4}-0]=\frac{1}{5}[ln 2^{4}]$
Hence, $\int_0^3\frac{dx}{5x+1}=\frac{4}{5}ln2$