Solve G ( x ) = ∫ (from 3 x to 2 x ^ 3) of 3t+5/2t-2dt

$$G ( x ) = \int _ { 3 x } ^ { 2 x ^ { 3 } } \frac { 3 t + 5 } { 2 t - 2 } d t$$

Evaluate

$$\left\{\begin{matrix}4\ln(|2x^{3}-1|)-4\ln(|3x-1|)+3x^{3}-\frac{9x}{2},&x>\frac{\sqrt{6}}{2}\text{ or }|x|=\frac{\sqrt{6}}{2}\text{ or }\left(x>-\frac{\sqrt{6}}{2}\text{ and }x\leq 0\right)\\\text{Indeterminate},&x>\frac{1}{3}\text{ and }x<\frac{2^{\frac{2}{3}}}{2}\\-4\ln(|2x^{3}-1|)+4\ln(|3x-1|)-3x^{3}+\frac{9x}{2},&x<-\frac{\sqrt{6}}{2}\text{ or }\left(x>0\text{ and }x<\frac{1}{3}\right)\text{ or }\left(x>\frac{2^{\frac{2}{3}}}{2}\text{ and }x<\frac{\sqrt{6}}{2}\right)\\\infty,&x=\frac{2^{\frac{2}{3}}}{2}\\-\infty,&x=\frac{1}{3}\end{matrix}\right.$$

Differentiate w.r.t. x

$$\text{Indeterminate}$$