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人気のある微分積分 >

integral of (1+4x)^{3/5}

解

\int (1 + 4 x)^{\frac{3}{5}} d x

解

\frac{5}{32} (1 + 4 x)^{\frac{8}{5}} + C

解答ステップ

\int (1 + 4 x)^{\frac{3}{5}} d x

u置換積分法を適用する

= \int \frac{u ^{\frac{3}{5}}}{4} d u

定数を除く:

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

= \frac{1}{4} \cdot \int u^{\frac{3}{5}} d u

べき乗則を適用する

= \frac{1}{4} \cdot \frac{5}{8} u^{\frac{8}{5}}

代用を戻す

u = 1 + 4 x

= \frac{1}{4} \cdot \frac{5}{8} (1 + 4 x)^{\frac{8}{5}}

簡素化

\frac{1}{4} \cdot \frac{5}{8} (1 + 4 x)^{\frac{8}{5}} : \frac{5}{32} (1 + 4 x)^{\frac{8}{5}}

= \frac{5}{32} (1 + 4 x)^{\frac{8}{5}}

定数を解答に追加する

= \frac{5}{32} (1 + 4 x)^{\frac{8}{5}} + C

グラフ

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