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人気のある微分積分 >

integral of xsqrt(4+x)

解

\int x 4 + x d x

解

\frac{2}{5} (4 + x)^{\frac{5}{2}} - \frac{8}{3} (4 + x)^{\frac{3}{2}} + C

解答ステップ

\int x 4 + x d x

u置換積分法を適用する

= \int (u - 4) u d u

拡張

(u - 4) u : u^{\frac{3}{2}} - 4 u

= \int u^{\frac{3}{2}} - 4 u d u

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{\frac{3}{2}} d u - \int 4 u d u

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

\int 4 u d u = \frac{8}{3} u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} - \frac{8}{3} u^{\frac{3}{2}}

代用を戻す

u = 4 + x

= \frac{2}{5} (4 + x)^{\frac{5}{2}} - \frac{8}{3} (4 + x)^{\frac{3}{2}}

定数を解答に追加する

= \frac{2}{5} (4 + x)^{\frac{5}{2}} - \frac{8}{3} (4 + x)^{\frac{3}{2}} + C

グラフ

人気の例

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