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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

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$$\int \dfrac{2^{x + 1} + 5^x}{10^x} dx=\int 2 \times5^{-x}+2^{-x} dx$$

$$=2\int e^{-\ln(5)x} dx+\int e^{-\ln(2)x} dx=-2\frac{5^{-x}}{\ln(5)}-\frac{2^{-x}}{\ln(2)}+C$$

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  • $\begingroup$ Yea, no problem lol $\endgroup$ – Ethan Jan 10 '14 at 12:18
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    $\begingroup$ $\int \dfrac{2^{x + 1} + 5^x}{10^x} dx=\int \frac{1}{2}5^{-x}+2^{-x} dx$ is wrong. The $\frac{1}{2}5^{-x}$ should be $2*5^{-x}$ $\endgroup$ – Kuai Jan 10 '14 at 12:25
  • $\begingroup$ @Kuai Thanks, fixed it $\endgroup$ – Ethan Jan 10 '14 at 12:26

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