integral from 1 to 4 of 3^{3x}

解答

\int_{1}^{4} 3^{3 x} d x

\frac{177138}{ln ( 3 )}

十进制

161237.95612 \dots

求解步骤

\int_{1}^{4} 3^{3 x} d x

化简

3^{3 x} : 2 7^{x}

= \int_{1}^{4} 2 7^{x} d x

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

= [\frac{2 7 ^{x}}{ln ( 27 )}]_{1}^{4}

\frac{2 7 ^{x}}{ln ( 27 )} = \frac{3 ^{3 x - 1}}{ln ( 3 )}

= [\frac{3 ^{3 x - 1}}{ln ( 3 )}]_{1}^{4}

带入上下限计算后得:

\frac{177138}{ln ( 3 )}

= \frac{177138}{ln ( 3 )}

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