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+7x-6)/((x+1)(x^2-4x+4))

Lösung

\int \frac{x ^{2} + 7 x - 6}{( x + 1 ) ( x ^{2} - 4 x + 4 )} d x

Lösung

- \frac{4}{3} ln ∣ x + 1 ∣ + \frac{7}{3} ln ∣ x - 2 ∣ - \frac{4}{x - 2} + C

Schritte zur Lösung

\int \frac{x ^{2} + 7 x - 6}{( x + 1 ) ( x ^{2} - 4 x + 4 )} d x

Ermittle den Partialbruch von

\frac{x ^{2} + 7 x - 6}{( x + 1 ) ( x ^{2} - 4 x + 4 )} : - \frac{4}{3 ( x + 1 )} + \frac{7}{3 ( x - 2 )} + \frac{4}{( x - 2 ) ^{2}}

= \int - \frac{4}{3 ( x + 1 )} + \frac{7}{3 ( x - 2 )} + \frac{4}{( x - 2 ) ^{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{4}{3 ( x + 1 )} d x + \int \frac{7}{3 ( x - 2 )} d x + \int \frac{4}{( x - 2 ) ^{2}} d x

\int \frac{4}{3 ( x + 1 )} d x = \frac{4}{3} ln ∣ x + 1 ∣

\int \frac{7}{3 ( x - 2 )} d x = \frac{7}{3} ln ∣ x - 2 ∣

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

= - \frac{4}{3} ln ∣ x + 1 ∣ + \frac{7}{3} ln ∣ x - 2 ∣ - \frac{4}{x - 2}

Füge eine Konstante zur Lösung hinzu

= - \frac{4}{3} ln ∣ x + 1 ∣ + \frac{7}{3} ln ∣ x - 2 ∣ - \frac{4}{x - 2} + C

Graph

Beliebte Beispiele

integral of \sqrt[4]{y}

\int 4 y d y

integral of x/((x-6))

\int \frac{x}{( x - 6 )} d x

integral of (y^2)/(sqrt(9-8y-y^2))

\int \frac{y ^{2}}{9 - 8 y - y ^{2}} d y

integral of (2t^{2/3}+sqrt(t))

\int (2 t^{\frac{2}{3}} + t) d t

integral of 2sin^2(3x)cos(3x)

\int 2 sin^{2} (3 x) cos (3 x) d x