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人気のある微分積分 >

integral of a^{5x}

解

\int a^{5 x} d x

解

\frac{a ^{5 x}}{5 ln ( a )} + C

解答ステップ

\int a^{5 x} d x

u置換積分法を適用する

= \int a^{u} \frac{1}{5} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int a^{u} d u

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

= \frac{1}{5} \cdot \frac{a ^{u}}{ln ( a )}

代用を戻す

u = 5 x

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

簡素化

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

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

定数を解答に追加する

= \frac{a ^{5 x}}{5 ln ( a )} + C

グラフ

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