Đáp án:

• Nhắc:   \( \int a^x \, dx = \frac{a^x}{\ln a} + c \)

• \( \int \frac{2^x - 1}{e^x} \, dx = \int \left[ \left( \frac{2}{e} \right)^x - \left( \frac{1}{e} \right)^x \right] dx \)

\( = \frac{\left( \frac{2}{e} \right)^x}{\ln \left( \frac{2}{e} \right)} - \frac{\left( \frac{1}{e} \right)^x}{\ln \left( \frac{1}{e} \right)} + c \)

\( = \frac{\left( \frac{2}{e} \right)^x}{\ln 2 - 1} - \frac{\left( \frac{1}{e} \right)^x}{-1} + c \)

\( = \frac{1}{\ln 2 - 1} \cdot \left( \frac{2}{e} \right)^x + \frac{1}{e^x} + c \)