Answer
$$\int^1_{-1}\frac{dx}{3x-4}=-\frac{\ln7}{3}$$
Work Step by Step
$$A=\int^1_{-1}\frac{dx}{3x-4}$$
We set $a=3x-4$, which means $$da=3dx$$ $$dx=\frac{1}{3}da$$
For $x=-1$, $a=-7$ and for $x=1$, $a=-1$
Therefore, $$A=\frac{1}{3}\int^{-1}_{-7} \frac{1}{a}da$$ $$A=\frac{1}{3}\Big(\ln|a|\Big]^{-1}_{-7}\Big)$$ $$A=\frac{1}{3}(\ln1-\ln7)$$ $$A=-\frac{\ln7}{3}$$
