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人気のある微分積分 >

integral from 1 to 25 of 5xe^{2x}

解

\int_{1}^{25} 5 x e^{2 x} d x

解

\frac{5 ( 49 e ^{50} - e ^{2} )}{4}

+1

十進法表記

3.17563 E 23

解答ステップ

\int_{1}^{25} 5 x e^{2 x} d x

定数を除く:

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

= 5 \cdot \int_{1}^{25} x e^{2 x} d x

u置換積分法を適用する

= 5 \cdot \int_{2}^{50} \frac{e ^{u} u}{4} d u

定数を除く:

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

= 5 \cdot \frac{1}{4} \cdot \int_{2}^{50} e^{u} u d u

部分積分を適用する

= 5 \cdot \frac{1}{4} [e^{u} u - \int e^{u} d u]_{2}^{50}

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

= 5 \cdot \frac{1}{4} [e^{u} u - e^{u}]_{2}^{50}

簡素化

5 \cdot \frac{1}{4} [e^{u} u - e^{u}]_{2}^{50} : \frac{5}{4} [e^{u} u - e^{u}]_{2}^{50}

= \frac{5}{4} [e^{u} u - e^{u}]_{2}^{50}

限度を計算する:

49 e^{50} - e^{2}

= \frac{5}{4} (49 e^{50} - e^{2})

簡素化

= \frac{5 ( 49 e ^{50} - e ^{2} )}{4}

グラフ

人気の例

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