Find $\int \frac{2^{x+1} - 5^{x-1}}{10^x} dx$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{1}{5 \cdot 2^x \ln 2} - \frac{2}{5^x \ln 5} + C$
$I = \int \left( 2(5^{-x}) - \frac{1}{5}(2^{-x}) \right) dx$
$= -\frac{2}{5^x \log 5} + \frac{1}{5(2^x) \log 2} + C$