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^2)/((x-1)^{20)}

解

\int \frac{x ^{2}}{( x - 1 ) ^{20}} d x

解

- \frac{1}{17 ( x - 1 ) ^{17}} - \frac{1}{9 ( x - 1 ) ^{18}} - \frac{1}{19 ( x - 1 ) ^{19}} + C

解答ステップ

\int \frac{x ^{2}}{( x - 1 ) ^{20}} d x

u置換積分法を適用する

= \int \frac{( u + 1 ) ^{2}}{u ^{20}} d u

拡張

\frac{( u + 1 ) ^{2}}{u ^{20}} : \frac{1}{u ^{18}} + \frac{2}{u ^{19}} + \frac{1}{u ^{20}}

= \int \frac{1}{u ^{18}} + \frac{2}{u ^{19}} + \frac{1}{u ^{20}} 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}{u ^{18}} d u + \int \frac{2}{u ^{19}} d u + \int \frac{1}{u ^{20}} d u

\int \frac{1}{u ^{18}} d u = - \frac{1}{17 u ^{17}}

\int \frac{2}{u ^{19}} d u = - \frac{1}{9 u ^{18}}

\int \frac{1}{u ^{20}} d u = - \frac{1}{19 u ^{19}}

= - \frac{1}{17 u ^{17}} - \frac{1}{9 u ^{18}} - \frac{1}{19 u ^{19}}

代用を戻す

u = x - 1

= - \frac{1}{17 ( x - 1 ) ^{17}} - \frac{1}{9 ( x - 1 ) ^{18}} - \frac{1}{19 ( x - 1 ) ^{19}}

定数を解答に追加する

= - \frac{1}{17 ( x - 1 ) ^{17}} - \frac{1}{9 ( x - 1 ) ^{18}} - \frac{1}{19 ( x - 1 ) ^{19}} + C

グラフ

人気の例

integral of 9/((1-8t)^7)

\int \frac{9}{( 1 - 8 t ) ^{7}} d t

integral of 4x^2+3x+5

\int 4 x^{2} + 3 x + 5 d x

integral of sin(x)sqrt(1-4cos^2(x))

\int sin (x) 1 - 4 cos^{2} (x) d x

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

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

integral of 5/(a+bx)

\int \frac{5}{a + b x} d x