de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (7x^2-9x+6)/((x-1)(x^2+1))

Lösung

\int \frac{7 x ^{2} - 9 x + 6}{( x - 1 ) ( x ^{2} + 1 )} d x

Lösung

2 ln ∣ x - 1 ∣ + \frac{5}{2} ln x^{2} + 1 - 4 arctan (x) + C

Schritte zur Lösung

\int \frac{7 x ^{2} - 9 x + 6}{( x - 1 ) ( x ^{2} + 1 )} d x

Ermittle den Partialbruch von

\frac{7 x ^{2} - 9 x + 6}{( x - 1 ) ( x ^{2} + 1 )} : \frac{2}{x - 1} + \frac{5 x - 4}{x ^{2} + 1}

= \int \frac{2}{x - 1} + \frac{5 x - 4}{x ^{2} + 1} 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{2}{x - 1} d x + \int \frac{5 x - 4}{x ^{2} + 1} d x

\int \frac{2}{x - 1} d x = 2 ln ∣ x - 1 ∣

\int \frac{5 x - 4}{x ^{2} + 1} d x = \frac{5}{2} ln x^{2} + 1 - 4 arctan (x)

= 2 ln ∣ x - 1 ∣ + \frac{5}{2} ln x^{2} + 1 - 4 arctan (x)

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x - 1 ∣ + \frac{5}{2} ln x^{2} + 1 - 4 arctan (x) + C

Graph

Beliebte Beispiele

integral of 19xsin(x)cos(x)

\int 19 x sin (x) cos (x) d x

integral of xex^2-1

\int x e x^{2} - 1 d x

integral of sin^4(7θ)

\int sin^{4} (7 θ) d θ

integral of (x^4)/(x^2+225)

\int \frac{x ^{4}}{x ^{2} + 225} d x

integral of e^{6x}(x^2-11x+1)

\int e^{6 x} (x^{2} - 11 x + 1) d x