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人気のある微分積分 >

integral of 2x^3\sqrt[5]{3x^4+7}

解

\int 2 x^{3} 5 3 x^{4} + 7 d x

解

\frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}} + C

解答ステップ

\int 2 x^{3} 5 3 x^{4} + 7 d x

定数を除く:

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

= 2 \cdot \int x^{3} 5 3 x^{4} + 7 d x

u置換積分法を適用する

= 2 \cdot \int \frac{5 u}{12} d u

定数を除く:

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

= 2 \cdot \frac{1}{12} \cdot \int 5 u d u

べき乗則を適用する

= 2 \cdot \frac{1}{12} \cdot \frac{5}{6} u^{\frac{6}{5}}

代用を戻す

u = 3 x^{4} + 7

= 2 \cdot \frac{1}{12} \cdot \frac{5}{6} (3 x^{4} + 7)^{\frac{6}{5}}

簡素化

2 \cdot \frac{1}{12} \cdot \frac{5}{6} (3 x^{4} + 7)^{\frac{6}{5}} : \frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}}

= \frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}}

定数を解答に追加する

= \frac{5}{36} (3 x^{4} + 7)^{\frac{6}{5}} + C

グラフ

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