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 p(p+7)^7

解

\int p (p + 7)^{7} d p

解

\frac{1}{72} (p + 7)^{8} (8 p - 7) + C

解答ステップ

\int p (p + 7)^{7} d p

u置換積分法を適用する

= \int \frac{7 u ( 7 u - 7 )}{7} d u

定数を除く:

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

= \frac{1}{7} \cdot \int 7 u (7 u - 7) d u

拡張

7 u (7 u - 7) : u^{\frac{2}{7}} - 7 7 u

= \frac{1}{7} \cdot \int u^{\frac{2}{7}} - 7 7 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

= \frac{1}{7} (\int u^{\frac{2}{7}} d u - \int 7 7 u d u)

\int u^{\frac{2}{7}} d u = \frac{7}{9} u^{\frac{9}{7}}

\int 7 7 u d u = \frac{49}{8} u^{\frac{8}{7}}

= \frac{1}{7} (\frac{7}{9} u^{\frac{9}{7}} - \frac{49}{8} u^{\frac{8}{7}})

代用を戻す

u = (p + 7)^{7}

= \frac{1}{7} (\frac{7}{9} ((p + 7)^{7})^{\frac{9}{7}} - \frac{49}{8} ((p + 7)^{7})^{\frac{8}{7}})

簡素化

\frac{1}{7} (\frac{7}{9} ((p + 7)^{7})^{\frac{9}{7}} - \frac{49}{8} ((p + 7)^{7})^{\frac{8}{7}}) : \frac{1}{72} (p + 7)^{8} (8 p - 7)

= \frac{1}{72} (p + 7)^{8} (8 p - 7)

定数を解答に追加する

= \frac{1}{72} (p + 7)^{8} (8 p - 7) + C

グラフ

人気の例

(\partial)/(\partial x)(y^6sin(6x))

\frac{\partial}{\partial x} (y^{6} sin (6 x))

integral of 1/(xsqrt(x^2+a^2))

\int \frac{1}{x x ^{2} + a ^{2}} d x

y^{^{'}} = x + 9 y

derivative of x^3cos(x-x^3sin(x))

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

limit as x approaches 2 of (x^2)/(2x-4)

x \to 2 lim (\frac{x ^{2}}{2 x - 4})