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$\int e^{\log _5 x} d x$ |
$\frac{x^{\log _5 e}}{\log _5 e}$ $\frac{x^{\log _5 5 e}}{\log _5 5 e}$ $\frac{x^{\log _e 5 e}+1}{\log _e 5 e+1}$ none of these |
$\frac{x^{\log _5 5 e}}{\log _5 5 e}$ |
$e^{\log _5 x}=x^{\log _5 e}$ (by property of exponential function) $\int e^{\log _5 x} d x=\int x^{\log _5 e} d x=\frac{x^{\log _5 5 e}+1}{\log _5 5 e+1}=\frac{x^{\log _5 5 e}}{\log _5 5 e}$ Hence (2) is the correct answer. |
