ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral of x\sqrt[3]{(x+3)^5}

解

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

解

\frac{3}{88} (8 x - 9) (x + 3)^{\frac{8}{3}} + C

解答ステップ

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

u置換積分法を適用する

= \int \frac{5 u - 3}{5 u ^{\frac{7}{15}}} d u

定数を除く:

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

= \frac{1}{5} \cdot \int \frac{5 u - 3}{u ^{\frac{7}{15}}} d u

拡張

\frac{5 u - 3}{u ^{\frac{7}{15}}} : \frac{1}{u ^{\frac{4}{15}}} - \frac{3}{u ^{\frac{7}{15}}}

= \frac{1}{5} \cdot \int \frac{1}{u ^{\frac{4}{15}}} - \frac{3}{u ^{\frac{7}{15}}} 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

= \frac{1}{5} (\int \frac{1}{u ^{\frac{4}{15}}} d u - \int \frac{3}{u ^{\frac{7}{15}}} d u)

\int \frac{1}{u ^{\frac{4}{15}}} d u = \frac{15}{11} u^{\frac{11}{15}}

\int \frac{3}{u ^{\frac{7}{15}}} d u = \frac{45}{8} u^{\frac{8}{15}}

= \frac{1}{5} (\frac{15}{11} u^{\frac{11}{15}} - \frac{45}{8} u^{\frac{8}{15}})

代用を戻す

u = (x + 3)^{5}

= \frac{1}{5} (\frac{15}{11} ((x + 3)^{5})^{\frac{11}{15}} - \frac{45}{8} ((x + 3)^{5})^{\frac{8}{15}})

簡素化

\frac{1}{5} (\frac{15}{11} ((x + 3)^{5})^{\frac{11}{15}} - \frac{45}{8} ((x + 3)^{5})^{\frac{8}{15}}) : \frac{3}{88} (8 x - 9) (x + 3)^{\frac{8}{3}}

= \frac{3}{88} (8 x - 9) (x + 3)^{\frac{8}{3}}

定数を解答に追加する

= \frac{3}{88} (8 x - 9) (x + 3)^{\frac{8}{3}} + C

グラフ

人気の例

derivative of-sin(3x3)

\frac{d}{d x} (- sin (3 x) 3)

integral of (2x+1)^{-1}

\int (2 x + 1)^{- 1} d x

limit as x approaches+0 of (2sin(2x))/x

x \to + 0 lim (\frac{2 sin ( 2 x )}{x})

integral of (x^2)/(sqrt(x^3+4))

\int \frac{x ^{2}}{x ^{3} + 4} d x

10y^{''}-7y^'-12y=0

10 y^{^{''}} - 7 y^{^{'}} - 12 y = 0