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人気のある微分積分 >

integral of 5x\sqrt[3]{(9-4x^2)^2}

解

\int 5 x 3 (9 - 4 x^{2})^{2} d x

解

- \frac{3}{8} (9 - 4 x^{2})^{\frac{5}{3}} + C

解答ステップ

\int 5 x 3 (9 - 4 x^{2})^{2} d x

定数を除く:

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

= 5 \cdot \int x 3 (9 - 4 x^{2})^{2} d x

u置換積分法を適用する

= 5 \cdot \int - \frac{u ^{\frac{2}{3}}}{8} d u

定数を除く:

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

= 5 (- \frac{1}{8} \cdot \int u^{\frac{2}{3}} d u)

べき乗則を適用する

= 5 (- \frac{1}{8} \cdot \frac{3}{5} u^{\frac{5}{3}})

代用を戻す

u = 9 - 4 x^{2}

= 5 (- \frac{1}{8} \cdot \frac{3}{5} (9 - 4 x^{2})^{\frac{5}{3}})

簡素化

5 (- \frac{1}{8} \cdot \frac{3}{5} (9 - 4 x^{2})^{\frac{5}{3}}) : - \frac{3}{8} (9 - 4 x^{2})^{\frac{5}{3}}

= - \frac{3}{8} (9 - 4 x^{2})^{\frac{5}{3}}

定数を解答に追加する

= - \frac{3}{8} (9 - 4 x^{2})^{\frac{5}{3}} + C

グラフ

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