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$If \int \frac{2^{x + 1} - 5^{x - 1}}{10^{x}} d x = = A \frac{{(\frac{1}{5})}^{x}}{\log (\frac{1}{5})} + B \frac{{(\frac{1}{2})}^{x}}{\log (\frac{1}{2})} + c t h e n$

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A=25, B=15

A=25, B=-15

A=2, B=-15

A=2, B=15

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Correct option is C

I=∫2x+1−5x−110xdx=∫5x 2x25x−15· 2x10xdx=∫215x−1512xdx=215xlog⁡15−1512xlog⁡12+c formula ∫axdx=axloge⁡a+c

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If ∫2x+1−5x−110xdx ==A15xlog⁡15+B12xlog⁡12+c then

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$If \int \frac{2^{x + 1} - 5^{x - 1}}{10^{x}} d x = = A \frac{{(\frac{1}{5})}^{x}}{\log (\frac{1}{5})} + B \frac{{(\frac{1}{2})}^{x}}{\log (\frac{1}{2})} + c t h e n$