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[9]{4+x^2}

解

\int x 9 4 + x^{2} d x

解

\frac{9}{20} (4 + x^{2})^{\frac{10}{9}} + C

解答ステップ

\int x 9 4 + x^{2} d x

u置換積分法を適用する

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

定数を除く:

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

= \frac{1}{2} \cdot \int 9 u d u

べき乗則を適用する

= \frac{1}{2} \cdot \frac{9}{10} u^{\frac{10}{9}}

代用を戻す

u = 4 + x^{2}

= \frac{1}{2} \cdot \frac{9}{10} (4 + x^{2})^{\frac{10}{9}}

簡素化

\frac{1}{2} \cdot \frac{9}{10} (4 + x^{2})^{\frac{10}{9}} : \frac{9}{20} (4 + x^{2})^{\frac{10}{9}}

= \frac{9}{20} (4 + x^{2})^{\frac{10}{9}}

定数を解答に追加する

= \frac{9}{20} (4 + x^{2})^{\frac{10}{9}} + C

グラフ

人気の例

inverselaplace (e^{-s})/(s^5)

in v erse l a pl a ce \frac{e ^{- s}}{s ^{5}}

limit as x approaches 0 of ((4^x-1))/x

x \to 0 lim (\frac{( 4 ^{x} - 1 )}{x})

integral of sin(7x-10)

\int sin (7 x - 10) d x

limit as x approaches infinity of 4x^3

x \to \infty lim (4 x^{3})

(\partial}{\partial y}(ln(\frac{x^2)/y))

\frac{\partial}{\partial y} (ln (\frac{x ^{2}}{y}))