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^3)/(x^2-36)

解

\int \frac{x ^{3}}{x ^{2} - 36} d x

解

\frac{1}{2} (x^{2} - 36 + 36 ln x^{2} - 36) + C

解答ステップ

\int \frac{x ^{3}}{x ^{2} - 36} d x

u置換積分法を適用する

= \int \frac{u + 36}{2 u} 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 \frac{u + 36}{u} d u

拡張

\frac{u + 36}{u} : 1 + \frac{36}{u}

= \frac{1}{2} \cdot \int 1 + \frac{36}{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}{2} (\int 1 d u + \int \frac{36}{u} d u)

\int 1 d u = u

\int \frac{36}{u} d u = 36 ln ∣ u ∣

= \frac{1}{2} (u + 36 ln ∣ u ∣)

代用を戻す

u = x^{2} - 36

= \frac{1}{2} (x^{2} - 36 + 36 ln x^{2} - 36)

定数を解答に追加する

= \frac{1}{2} (x^{2} - 36 + 36 ln x^{2} - 36) + C

グラフ

人気の例

integral of sqrt(y/3)

\int \frac{y}{3} d y

integral from 0 to 1 of (10y)/(e^{2y)}

\int_{0}^{1} \frac{10 y}{e ^{2 y}} d y

(\partial)/(\partial y)(((ax+by))/(cx+dy))

\frac{\partial}{\partial y} (\frac{( a x + b y )}{c x + d y})

integral from 0 to infinity of x/(x^3+1)

\int_{0}^{\infty} \frac{x}{x ^{3} + 1} d x

limit as x approaches 3 of (4x-5)/(5x-1)

x \to 3 lim (\frac{4 x - 5}{5 x - 1})