integral from 2 to 5 of 5^{2x}

解答

\int_{2}^{5} 5^{2 x} d x

\frac{4882500}{ln ( 5 )}

十进制

3033667.81798 \dots

求解步骤

\int_{2}^{5} 5^{2 x} d x

化简

5^{2 x} : 2 5^{x}

= \int_{2}^{5} 2 5^{x} d x

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

= [\frac{2 5 ^{x}}{ln ( 25 )}]_{2}^{5}

化简

ln (25) : 2 ln (5)

= [\frac{2 5 ^{x}}{2 ln ( 5 )}]_{2}^{5}

带入上下限计算后得:

\frac{4882500}{ln ( 5 )}

= \frac{4882500}{ln ( 5 )}

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