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^4))/((x-1)^2(x+2))

Lösung

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

Lösung

\frac{x ^{2}}{2} + \frac{11}{9} ln ∣ x - 1 ∣ - \frac{1}{3 ( x - 1 )} + \frac{16}{9} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x ^{4}}{( x - 1 ) ^{2} ( x + 2 )} : x + \frac{11}{9 ( x - 1 )} + \frac{1}{3 ( x - 1 ) ^{2}} + \frac{16}{9 ( x + 2 )}

= \int x + \frac{11}{9 ( x - 1 )} + \frac{1}{3 ( x - 1 ) ^{2}} + \frac{16}{9 ( x + 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 x d x + \int \frac{11}{9 ( x - 1 )} d x + \int \frac{1}{3 ( x - 1 ) ^{2}} d x + \int \frac{16}{9 ( x + 2 )} d x

\int x d x = \frac{x ^{2}}{2}

\int \frac{11}{9 ( x - 1 )} d x = \frac{11}{9} ln ∣ x - 1 ∣

\int \frac{1}{3 ( x - 1 ) ^{2}} d x = - \frac{1}{3 ( x - 1 )}

\int \frac{16}{9 ( x + 2 )} d x = \frac{16}{9} ln ∣ x + 2 ∣

= \frac{x ^{2}}{2} + \frac{11}{9} ln ∣ x - 1 ∣ - \frac{1}{3 ( x - 1 )} + \frac{16}{9} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + \frac{11}{9} ln ∣ x - 1 ∣ - \frac{1}{3 ( x - 1 )} + \frac{16}{9} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of 3x^2(2-x^3)^8

\int 3 x^{2} (2 - x^{3})^{8} d x

integral of (e^x)/((e^x-6)(e^x+1))

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

integral of (ln(x^2))/(3x)

\int \frac{ln ( x ^{2} )}{3 x} d x

integral of e^{(e^x+x)}

\int e^{(e^{x} + x)} d x

integral of x^5+x+3

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