# Cannot solve indefinite integral

can You help me with this indefinite integral

$$\int \dfrac{2^{x + 1} + 5^x}{10^x} dx$$

What to use. direct integration or substitute of variables Thanks

$$\int \dfrac{2^{x + 1} + 5^x}{10^x} dx=\int 2 \times5^{-x}+2^{-x} dx$$
$$=2\int e^{-\ln(5)x} dx+\int e^{-\ln(2)x} dx=-2\frac{5^{-x}}{\ln(5)}-\frac{2^{-x}}{\ln(2)}+C$$
• $\int \dfrac{2^{x + 1} + 5^x}{10^x} dx=\int \frac{1}{2}5^{-x}+2^{-x} dx$ is wrong. The $\frac{1}{2}5^{-x}$ should be $2*5^{-x}$ – Kuai Jan 10 '14 at 12:25