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/(x^2-36)

解

\int \frac{1}{x ^{2} - 36} d x

解

- \frac{1}{12} (ln \frac{x}{6} + 1 - ln \frac{x}{6} - 1) + C

解答ステップ

\int \frac{1}{x ^{2} - 36} d x

置換積分法を適用する

= \int \frac{1}{6 ( u ^{2} - 1 )} d u

定数を除く:

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

= \frac{1}{6} \cdot \int \frac{1}{u ^{2} - 1} d u

因数

u^{2} - 1 : - (- u^{2} + 1)

= \frac{1}{6} \cdot \int \frac{1}{- ( - u ^{2} + 1 )} d u

定数を除く:

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

= \frac{1}{6} (- \int \frac{1}{- u ^{2} + 1} d u)

共通積分を使用する:

\int \frac{1}{- u ^{2} + 1} d u = \frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}

= \frac{1}{6} (- (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}))

代用を戻す

u = \frac{x}{6}

= \frac{1}{6} (- (\frac{ln \frac{x}{6} + 1}{2} - \frac{ln \frac{x}{6} - 1}{2}))

簡素化

\frac{1}{6} (- (\frac{ln \frac{x}{6} + 1}{2} - \frac{ln \frac{x}{6} - 1}{2})) : - \frac{1}{12} (ln \frac{x}{6} + 1 - ln \frac{x}{6} - 1)

= - \frac{1}{12} (ln \frac{x}{6} + 1 - ln \frac{x}{6} - 1)

定数を解答に追加する

= - \frac{1}{12} (ln \frac{x}{6} + 1 - ln \frac{x}{6} - 1) + C

グラフ

人気の例

derivative of ((x^2+2x+1)/((x^2-2x+1)))

\frac{d}{d x} (\frac{( x ^{2} + 2 x + 1 )}{( x ^{2} - 2 x + 1 )})

y^{^{'}} = - a \cdot y^{2}

\frac{d}{d t} (t^{9} e^{t})

4^{^{'}}

integral of 8/(xsqrt(64-(ln(x))^2))

\int \frac{8}{x 64 - ( ln ( x ) ) ^{2}} d x