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(1-x)^{99}

解

\int x (1 - x)^{99} d x

解

\frac{1}{101} (1 - x)^{101} - \frac{1}{100} (1 - x)^{100} + C

解答ステップ

\int x (1 - x)^{99} d x

u置換積分法を適用する

= \int - (- u + 1) u^{99} d u

定数を除く:

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

= - \int (- u + 1) u^{99} d u

拡張

(- u + 1) u^{99} : - u^{100} + u^{99}

= - \int - u^{100} + u^{99} 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^{100} d u + \int u^{99} d u)

\int u^{100} d u = \frac{u ^{101}}{101}

\int u^{99} d u = \frac{u ^{100}}{100}

= - (- \frac{u ^{101}}{101} + \frac{u ^{100}}{100})

代用を戻す

u = 1 - x

= - (- \frac{( 1 - x ) ^{101}}{101} + \frac{( 1 - x ) ^{100}}{100})

簡素化

- (- \frac{( 1 - x ) ^{101}}{101} + \frac{( 1 - x ) ^{100}}{100}) : \frac{1}{101} (1 - x)^{101} - \frac{1}{100} (1 - x)^{100}

= \frac{1}{101} (1 - x)^{101} - \frac{1}{100} (1 - x)^{100}

定数を解答に追加する

= \frac{1}{101} (1 - x)^{101} - \frac{1}{100} (1 - x)^{100} + C

グラフ

人気の例

integral of x/(x^4+4x^2+5)

\int \frac{x}{x ^{4} + 4 x ^{2} + 5} d x

limit as x approaches 2+of (2-x)/(|x-2|)

x \to 2 + lim (\frac{2 - x}{∣ x - 2 ∣})

limit as t approaches 0 of (e^{1/t})/t

t \to 0 lim (\frac{e ^{\frac{1}{t}}}{t})

implicit (dy)/(dx),2x^3-5xy-y^2=3

im pl i c i t \frac{d y}{d x}, 2 x^{3} - 5 x y - y^{2} = 3

limit as x approaches-2 of (6x+1)(2x-3)

x \to - 2 lim ((6 x + 1) (2 x - 3))