Spočtěte neurčitý integrál \displaystyle\int\frac{x\cdot 2^x+1}{8x}dx.

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Spočtěte neurčitý integrál

\displaystyle\int\frac{x\cdot 2^x+1}{8x}dx.

\displaystyle\frac{x^2\cdot 2^x\cdot \ln2-1}{8x^2}+C

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\displaystyle\frac{x\cdot 2^x+2\ln2}{8x\cdot \ln 2}+C

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\displaystyle\frac{2^x+\ln2\cdot \ln |x|}{8\ln 2}+C

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\displaystyle\frac{(x-1)2^x+x}{4x^2}+C

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\displaystyle\frac{2^x+x\cdot 2^x\cdot \ln2}{8}+C

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\displaystyle\frac{2^x+2(x-1)}{8(x-1)}+C

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