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 7/((x-1)(x+6))

解

\int \frac{7}{( x - 1 ) ( x + 6 )} d x

解

ln ∣ x - 1 ∣ - ln ∣ x + 6 ∣ + C

解答ステップ

\int \frac{7}{( x - 1 ) ( x + 6 )} d x

定数を除く:

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

= 7 \cdot \int \frac{1}{( x - 1 ) ( x + 6 )} d x

以下の部分分数を得る:

\frac{1}{( x - 1 ) ( x + 6 )} : \frac{1}{7 ( x - 1 )} - \frac{1}{7 ( x + 6 )}

= 7 \cdot \int \frac{1}{7 ( x - 1 )} - \frac{1}{7 ( x + 6 )} d x

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

= 7 (\int \frac{1}{7 ( x - 1 )} d x - \int \frac{1}{7 ( x + 6 )} d x)

\int \frac{1}{7 ( x - 1 )} d x = \frac{1}{7} ln ∣ x - 1 ∣

\int \frac{1}{7 ( x + 6 )} d x = \frac{1}{7} ln ∣ x + 6 ∣

= 7 (\frac{1}{7} ln ∣ x - 1 ∣ - \frac{1}{7} ln ∣ x + 6 ∣)

簡素化

7 (\frac{1}{7} ln ∣ x - 1 ∣ - \frac{1}{7} ln ∣ x + 6 ∣) : ln ∣ x - 1 ∣ - ln ∣ x + 6 ∣

= ln ∣ x - 1 ∣ - ln ∣ x + 6 ∣

定数を解答に追加する

= ln ∣ x - 1 ∣ - ln ∣ x + 6 ∣ + C

グラフ

人気の例

integral of (sec^2(x))/((tan(x)+pi)^3)

\int \frac{sec ^{2} ( x )}{( tan ( x ) + π ) ^{3}} d x

integral of (x^2+2x+1)/(x^4+2x^2+1)

\int \frac{x ^{2} + 2 x + 1}{x ^{4} + 2 x ^{2} + 1} d x

integral of ln(x)+tan(x)

\int ln (x) + tan (x) d x

integral of (x+3)/(x^4+1)

\int \frac{x + 3}{x ^{4} + 1} d x

integral of (e^t)/(4+e^t)

\int \frac{e ^{t}}{4 + e ^{t}} d t