de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^2)/((x-6)(x-7)^2)

Lösung

\int \frac{x ^{2}}{( x - 6 ) ( x - 7 ) ^{2}} d x

Lösung

36 ln ∣ x - 6 ∣ - 35 ln ∣ x - 7 ∣ - \frac{49}{x - 7} + C

Schritte zur Lösung

\int \frac{x ^{2}}{( x - 6 ) ( x - 7 ) ^{2}} d x

Ermittle den Partialbruch von

\frac{x ^{2}}{( x - 6 ) ( x - 7 ) ^{2}} : \frac{36}{x - 6} - \frac{35}{x - 7} + \frac{49}{( x - 7 ) ^{2}}

= \int \frac{36}{x - 6} - \frac{35}{x - 7} + \frac{49}{( x - 7 ) ^{2}} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{36}{x - 6} d x - \int \frac{35}{x - 7} d x + \int \frac{49}{( x - 7 ) ^{2}} d x

\int \frac{36}{x - 6} d x = 36 ln ∣ x - 6 ∣

\int \frac{35}{x - 7} d x = 35 ln ∣ x - 7 ∣

\int \frac{49}{( x - 7 ) ^{2}} d x = - \frac{49}{x - 7}

= 36 ln ∣ x - 6 ∣ - 35 ln ∣ x - 7 ∣ - \frac{49}{x - 7}

Füge eine Konstante zur Lösung hinzu

= 36 ln ∣ x - 6 ∣ - 35 ln ∣ x - 7 ∣ - \frac{49}{x - 7} + C

Graph

Beliebte Beispiele

laplacetransform te^{7t}

l a pl a ce t r an s f or m t e^{7 t}

(dy)/(dt)=3y+y^5,y(0)=1

\frac{d y}{d t} = 3 y + y^{5}, y (0) = 1

integral of xsec(3x^2+1)

\int x sec (3 x^{2} + 1) d x

6(dy)/(dx)-2y=xy^4,y(0)=-2

6 \frac{d y}{d x} - 2 y = x y^{4}, y (0) = - 2

((2y)/x+2x)+(2ln(x)-3)((dy)/(dx))=0

(\frac{2 y}{x} + 2 x) + (2 ln (x) - 3) (\frac{d y}{d x}) = 0