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 (4-x^2)^{3/2}x

解

\int (4 - x^{2})^{\frac{3}{2}} x d x

解

- \frac{1}{5} (4 - x^{2})^{\frac{5}{2}} + C

解答ステップ

\int (4 - x^{2})^{\frac{3}{2}} x d x

u置換積分法を適用する

= \int - \frac{u ^{\frac{3}{2}}}{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 u^{\frac{3}{2}} d u

べき乗則を適用する

= - \frac{1}{2} \cdot \frac{2}{5} u^{\frac{5}{2}}

代用を戻す

u = 4 - x^{2}

= - \frac{1}{2} \cdot \frac{2}{5} (4 - x^{2})^{\frac{5}{2}}

簡素化

- \frac{1}{2} \cdot \frac{2}{5} (4 - x^{2})^{\frac{5}{2}} : - \frac{1}{5} (4 - x^{2})^{\frac{5}{2}}

= - \frac{1}{5} (4 - x^{2})^{\frac{5}{2}}

定数を解答に追加する

= - \frac{1}{5} (4 - x^{2})^{\frac{5}{2}} + C

グラフ

人気の例

derivative of (xx^2cos(x))

\frac{d}{d x} ((x) x^{2} cos (x))

limit as x approaches 0 of (1+2x)^{6/x}

x \to 0 lim ((1 + 2 x)^{\frac{6}{x}})

sum from n=2 to infinity of ln(ln(n))

n = 2 \sum \infty ln (ln (n))

limit as x approaches 3 of sqrt(3x-5)

x \to 3 lim (3 x - 5)

integral of+tln(t+5)

\int + t ln (t + 5) d t