[tex]\displaystyle \int\limits \frac{3\cdot 2^x-2\cdot 3^x}{2^x} \, dx = 3\int\limits\, dx -2\int\limits\bigg(\frac{3}{2}\bigg)^x\, dx = 3x-\frac{2\cdot\big(\frac{3}{2}\big)^x}{ln\big(\frac{3}{2}\big)} + C[/tex]