integral from 2 to 4 of 4^{3x}

解答

\int_{2}^{4} 4^{3 x} d x

\frac{2795520}{ln ( 2 )}

十进制

4033082.84070 \dots

求解步骤

\int_{2}^{4} 4^{3 x} d x

化简

4^{3 x} : 6 4^{x}

= \int_{2}^{4} 6 4^{x} d x

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

= [\frac{6 4 ^{x}}{ln ( 64 )}]_{2}^{4}

\frac{6 4 ^{x}}{ln ( 64 )} = \frac{2 ^{6 x - 1}}{3 ln ( 2 )}

= [\frac{2 ^{6 x - 1}}{3 ln ( 2 )}]_{2}^{4}

带入上下限计算后得:

\frac{2795520}{ln ( 2 )}

= \frac{2795520}{ln ( 2 )}

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