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人気のある微分積分 >

integral of \sqrt[3]{3-4x^2}(-8x)

解

\int 3 3 - 4 x^{2} (- 8 x) d x

解

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

解答ステップ

\int 3 3 - 4 x^{2} (- 8 x) d x

簡素化

= \int - 8 x 3 3 - 4 x^{2} d x

定数を除く:

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

= - 8 \cdot \int x 3 3 - 4 x^{2} d x

u置換積分法を適用する

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

定数を除く:

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

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

べき乗則を適用する

= - 8 (- \frac{1}{8} \cdot \frac{3}{4} u^{\frac{4}{3}})

代用を戻す

u = 3 - 4 x^{2}

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

簡素化

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

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

定数を解答に追加する

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

グラフ

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