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 1/((60-x)(150-x))

解

\int \frac{1}{( 60 - x ) ( 150 - x )} d x

解

- \frac{1}{90} ln ∣ 60 - x ∣ + \frac{1}{90} ln ∣ - x + 150 ∣ + C

解答ステップ

\int \frac{1}{( 60 - x ) ( 150 - x )} d x

u置換積分法を適用する

= \int - \frac{1}{u ( u + 90 )} d u

定数を除く:

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

= - \int \frac{1}{u ( u + 90 )} d u

以下の部分分数を得る:

\frac{1}{u ( u + 90 )} : \frac{1}{90 u} - \frac{1}{90 ( u + 90 )}

= - \int \frac{1}{90 u} - \frac{1}{90 ( u + 90 )} 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 \frac{1}{90 u} d u - \int \frac{1}{90 ( u + 90 )} d u)

\int \frac{1}{90 u} d u = \frac{1}{90} ln ∣ u ∣

\int \frac{1}{90 ( u + 90 )} d u = \frac{1}{90} ln ∣ u + 90 ∣

= - (\frac{1}{90} ln ∣ u ∣ - \frac{1}{90} ln ∣ u + 90 ∣)

代用を戻す

u = 60 - x

= - (\frac{1}{90} ln ∣ 60 - x ∣ - \frac{1}{90} ln ∣ 60 - x + 90 ∣)

簡素化

- (\frac{1}{90} ln ∣ 60 - x ∣ - \frac{1}{90} ln ∣ 60 - x + 90 ∣) : - \frac{1}{90} ln ∣ 60 - x ∣ + \frac{1}{90} ln ∣ - x + 150 ∣

= - \frac{1}{90} ln ∣ 60 - x ∣ + \frac{1}{90} ln ∣ - x + 150 ∣

定数を解答に追加する

= - \frac{1}{90} ln ∣ 60 - x ∣ + \frac{1}{90} ln ∣ - x + 150 ∣ + C

グラフ

人気の例

integral of ((cos(x)))/((4-sin^2(x)))

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

integral of y^{-1}+3/x

\int y^{- 1} + \frac{3}{x} d x

integral of (6x^2)(x^{1/4})

\int (6 x^{2}) (x^{\frac{1}{4}}) d x

integral of 1/(6x+2)

\int \frac{1}{6 x + 2} d x

integral of 8/7 \sqrt[7]{x}

\int \frac{8}{7} 7 x d x