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人気のある微分積分 >

integral of sqrt(x^2-2x^4)

解

\int x^{2} - 2 x^{4} d x

解

- \frac{1}{6} (1 - 2 x^{2})^{\frac{3}{2}} + C

解答ステップ

\int x^{2} - 2 x^{4} d x

簡素化

x^{2} - 2 x^{4} : x^{2} 1 - 2 x^{2}

= \int x^{2} 1 - 2 x^{2} d x

x^{2} = (x), （ x \geq 0

と仮定

）

= \int x 1 - 2 x^{2} d x

u置換積分法を適用する

= \int - \frac{u}{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 d u

べき乗則を適用する

= - \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

代用を戻す

u = 1 - 2 x^{2}

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

簡素化

- \frac{1}{4} \cdot \frac{2}{3} (1 - 2 x^{2})^{\frac{3}{2}} : - \frac{1}{6} (1 - 2 x^{2})^{\frac{3}{2}}

= - \frac{1}{6} (1 - 2 x^{2})^{\frac{3}{2}}

定数を解答に追加する

= - \frac{1}{6} (1 - 2 x^{2})^{\frac{3}{2}} + C

グラフ

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