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

解

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

\frac{43680}{ln ( 2 )}

十進法表記

63016.91938 \dots

解答ステップ

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

簡素化

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

= \int_{1}^{3} 6 4^{x} d x

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

= [\frac{6 4 ^{x}}{ln ( 64 )}]_{1}^{3}

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

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

限度を計算する:

\frac{43680}{ln ( 2 )}

= \frac{43680}{ln ( 2 )}