integral from 0 to 1 of 4^{5x}

解答

\int_{0}^{1} 4^{5 x} d x

\frac{1023}{10 ln ( 2 )}

十进制

147.58770 \dots

求解步骤

\int_{0}^{1} 4^{5 x} d x

化简

4^{5 x} : 102 4^{x}

= \int_{0}^{1} 102 4^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{102 4 ^{x}}{ln ( 1024 )}]_{0}^{1}

\frac{102 4 ^{x}}{ln ( 1024 )} = \frac{2 ^{10 x - 1}}{5 ln ( 2 )}

= [\frac{2 ^{10 x - 1}}{5 ln ( 2 )}]_{0}^{1}

带入上下限计算后得:

\frac{1023}{10 ln ( 2 )}

= \frac{1023}{10 ln ( 2 )}

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