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人気のある微分積分 >

integral from 0 to ln(3) of 3e^{3x}

解

\int_{0}^{l n (3)} 3 e^{3 x} d x

解

26

解答ステップ

\int_{0}^{l n (3)} 3 e^{3 x} d x

定数を除く:

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

= 3 \cdot \int_{0}^{l n (3)} e^{3 x} d x

u置換積分法を適用する

= 3 \cdot \int_{0}^{3 l n (3)} e^{u} \frac{1}{3} d u

定数を除く:

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

= 3 \cdot \frac{1}{3} \cdot \int_{0}^{3 l n (3)} e^{u} d u

共通積分を使用する:

\int e^{u} d u = e^{u}

= 3 \cdot \frac{1}{3} [e^{u}]_{0}^{3 l n (3)}

簡素化

3 \cdot \frac{1}{3} [e^{u}]_{0}^{3 l n (3)} : [e^{u}]_{0}^{3 l n (3)}

= [e^{u}]_{0}^{3 l n (3)}

限度を計算する:

26

= 26

グラフ

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