Ta có:
$\int\dfrac{3^x+9.5^x}{7^x}dx$
$=\int\left(\left(\dfrac{3}{7}\right)^x+9\left(\dfrac{5}{7}\right)^x\right)dx$
$=\dfrac{1}{\ln\frac{3}{7}}\left(\dfrac{3}{7}\right)^x+\dfrac{9}{\ln\frac{5}{7}}\left(\dfrac{5}{7}\right)^x+C$
$=\dfrac{1}{\ln3-\ln7}\left(\dfrac{3}{7}\right)^x+\dfrac{9}{\ln5-\ln7}\left(\dfrac{5}{7}\right)^x+C$