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 w/((1+w)^{3/4)}

解

\int \frac{w}{( 1 + w ) ^{\frac{3}{4}}} d w

解

\frac{4}{5} (1 + w)^{\frac{5}{4}} - 4 (1 + w)^{\frac{1}{4}} + C

解答ステップ

\int \frac{w}{( 1 + w ) ^{\frac{3}{4}}} d w

u置換積分法を適用する

= \int \frac{u - 1}{u ^{\frac{3}{4}}} d u

拡張

\frac{u - 1}{u ^{\frac{3}{4}}} : u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}}

= \int u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}} 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{1}{4}} d u - \int \frac{1}{u ^{\frac{3}{4}}} d u

\int u^{\frac{1}{4}} d u = \frac{4}{5} u^{\frac{5}{4}}

\int \frac{1}{u ^{\frac{3}{4}}} d u = 4 u^{\frac{1}{4}}

= \frac{4}{5} u^{\frac{5}{4}} - 4 u^{\frac{1}{4}}

代用を戻す

u = 1 + w

= \frac{4}{5} (1 + w)^{\frac{5}{4}} - 4 (1 + w)^{\frac{1}{4}}

定数を解答に追加する

= \frac{4}{5} (1 + w)^{\frac{5}{4}} - 4 (1 + w)^{\frac{1}{4}} + C

グラフ

人気の例

limit as x approaches 0 of 4/(sin(5x))

x \to 0 lim (\frac{4}{sin ( 5 x )})

y^{^{'}} = - x e^{- x + y}

integral of ((3x+5))/(x^2+2x+1)

\int \frac{( 3 x + 5 )}{x ^{2} + 2 x + 1} d x

(\partial)/(\partial x)(x+4)

\frac{\partial}{\partial x} (x + 4)

limit as x approaches 5 of-x^2+9x-7

x \to 5 lim (- x^{2} + 9 x - 7)