Answer
$\frac{1}{3}\ln\frac{8}{5}$
Work Step by Step
Using the fact that $\frac{u'}{u}=\ln u $, we have
$$\int_2^{4} \frac{1}{3t+4}dt=\frac{1}{3}\int_2^{4} \frac{3}{3t+4}dt=\frac{1}{3}\ln (3t+4)|_2^{4}\\
=\frac{1}{3}(\ln 16-\ln 10)=\frac{1}{3}\ln \frac{16}{10}=\frac{1}{3}\ln\frac{8}{5}. $$
where used the property:
$\ln A-\ln B=\frac{A}{B}$.
