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人気のある微分積分 >

integral of ((x^2+7)^{2021})x

解

\int ((x^{2} + 7)^{2021}) x d x

解

\frac{1}{4044} (x^{2} + 7)^{2022} + C

解答ステップ

\int (x^{2} + 7)^{2021} x d x

u置換積分法を適用する

= \int \frac{u ^{2021}}{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 u^{2021} d u

べき乗則を適用する

= \frac{1}{2} \cdot \frac{u ^{2022}}{2022}

代用を戻す

u = x^{2} + 7

= \frac{1}{2} \cdot \frac{( x ^{2} + 7 ) ^{2022}}{2022}

簡素化

\frac{1}{2} \cdot \frac{( x ^{2} + 7 ) ^{2022}}{2022} : \frac{1}{4044} (x^{2} + 7)^{2022}

= \frac{1}{4044} (x^{2} + 7)^{2022}

定数を解答に追加する

= \frac{1}{4044} (x^{2} + 7)^{2022} + C

グラフ

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