CUET Preparation Today
Find $\int \frac{2^{x+1} - 5^{x-1}}{10^x} dx$. |
$\frac{2 \cdot 5^{-x}}{\ln 5} - \frac{2^{-x}}{5 \ln 2} + C$ $\frac{1}{5 \cdot 2^x \ln 2} - \frac{2}{5^x \ln 5} + C$ $\frac{1}{2^x \ln 2} - \frac{1}{5^x \ln 5} + C$ $-\frac{2}{5^x \ln 5} - \frac{1}{5 \cdot 2^x \ln 2} + C$ |
$\frac{1}{5 \cdot 2^x \ln 2} - \frac{2}{5^x \ln 5} + C$ |
The correct answer is Option (2) → $\frac{1}{5 \cdot 2^x \ln 2} - \frac{2}{5^x \ln 5} + C$ $I = \int \left( 2(5^{-x}) - \frac{1}{5}(2^{-x}) \right) dx$ $= -\frac{2}{5^x \log 5} + \frac{1}{5(2^x) \log 2} + C$ |
