Question

Evaluate $\int \frac{2^{x+1}-5^{x-1}}{{10}^x}$ dx

Answer 1

$\frac{2^{x+1}}{{10}^x}-\frac{5^{x-1}}{{10}^x}$

=> ${2.5}^{-x}-\frac{2^{-x}}{5}$

Hence

$\int {2.5}^{-x}-\int 2^{-x}/5$

$\frac{log2\times 2^{-x}}{5}-\left(2log5\right)\left(5^{-x}\right)+C$