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

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15log⁡22x+1−2log⁡55x−1+C

2(x+1)5x+1−x2x+C

2(x+1)5x+1+x2x+C

15log⁡22−x−2log⁡55−x+C

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detailed solution

Correct option is D

∫2x+1−5x−110xdx=∫210x⋅2−510x15dx=2∫15xdx−15∫12xdx=25−x−log⁡5+152−xlog⁡2+C

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∫2x+1−5x−110xdx equals

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