Question:

$$\int \frac{2^x + 3^{2x+1} + 5^{3x-2}}{7^x} dx = \int \left( \left(\frac{2}{7}\right)^x + 3\left(\frac{9}{7}\right)^x + \frac{1}{25}\left(\frac{125}{7}\right)^x \right) dx = \frac{\left(\frac{2}{7}\right)^x}{\ln\left(\frac{2}{7}\right)} + 3 \frac{\left(\frac{9}{7}\right)^x}{\ln\left(\frac{9}{7}\right)} + \frac{1}{25} \frac{\left(\frac{125}{7}\right)^x}{\ln\left(\frac{125}{7}\right)} + C$$