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人気のある微分積分 >

integral from 1 to 5 of x(4+x^2)^{10}

解

\int_{1}^{5} x (4 + x^{2})^{10} d x

解

\frac{2 9 ^{11} - 48828125}{22}

+1

十進法表記

5.54569 E 14

解答ステップ

\int_{1}^{5} x (4 + x^{2})^{10} d x

u置換積分法を適用する

= \int_{5}^{29} \frac{u ^{10}}{2} d u

定数を除く:

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

= \frac{1}{2} \cdot \int_{5}^{29} u^{10} d u

べき乗則を適用する

= \frac{1}{2} [\frac{u ^{11}}{11}]_{5}^{29}

限度を計算する:

\frac{2 9 ^{11}}{11} - \frac{48828125}{11}

= \frac{1}{2} (\frac{2 9 ^{11}}{11} - \frac{48828125}{11})

簡素化

= \frac{2 9 ^{11} - 48828125}{22}

グラフ

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