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人気のある微分積分 >

integral of x^6(x^7-3)^{3/4}

解

\int x^{6} (x^{7} - 3)^{\frac{3}{4}} d x

解

\frac{4}{49} (x^{7} - 3)^{\frac{7}{4}} + C

解答ステップ

\int x^{6} (x^{7} - 3)^{\frac{3}{4}} d x

u置換積分法を適用する

= \int \frac{u ^{\frac{3}{4}}}{7} d u

定数を除く:

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

= \frac{1}{7} \cdot \int u^{\frac{3}{4}} d u

べき乗則を適用する

= \frac{1}{7} \cdot \frac{4}{7} u^{\frac{7}{4}}

代用を戻す

u = x^{7} - 3

= \frac{1}{7} \cdot \frac{4}{7} (x^{7} - 3)^{\frac{7}{4}}

簡素化

\frac{1}{7} \cdot \frac{4}{7} (x^{7} - 3)^{\frac{7}{4}} : \frac{4}{49} (x^{7} - 3)^{\frac{7}{4}}

= \frac{4}{49} (x^{7} - 3)^{\frac{7}{4}}

定数を解答に追加する

= \frac{4}{49} (x^{7} - 3)^{\frac{7}{4}} + C

グラフ

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