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人気のある微分積分 >

integral of (1/5)^x

解

\int (\frac{1}{5})^{x} d x

解

- \frac{1}{ln ( 5 ) \cdot 5 ^{x}} + C

解答ステップ

\int (\frac{1}{5})^{x} d x

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

= \frac{( \frac{1}{5} ) ^{x}}{ln ( \frac{1}{5} )}

簡素化

\frac{( \frac{1}{5} ) ^{x}}{ln ( \frac{1}{5} )} : - \frac{1}{ln ( 5 ) \cdot 5 ^{x}}

= - \frac{1}{ln ( 5 ) \cdot 5 ^{x}}

定数を解答に追加する

= - \frac{1}{ln ( 5 ) \cdot 5 ^{x}} + C

グラフ

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