de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (6x^2+5x+59)/((x+1)(x^2+9))

Lösung

\int \frac{6 x ^{2} + 5 x + 59}{( x + 1 ) ( x ^{2} + 9 )} d x

Lösung

6 ln ∣ x + 1 ∣ + \frac{5}{3} arctan (\frac{x}{3}) + C

Schritte zur Lösung

\int \frac{6 x ^{2} + 5 x + 59}{( x + 1 ) ( x ^{2} + 9 )} d x

Ermittle den Partialbruch von

\frac{6 x ^{2} + 5 x + 59}{( x + 1 ) ( x ^{2} + 9 )} : \frac{6}{x + 1} + \frac{5}{x ^{2} + 9}

= \int \frac{6}{x + 1} + \frac{5}{x ^{2} + 9} 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{6}{x + 1} d x + \int \frac{5}{x ^{2} + 9} d x

\int \frac{6}{x + 1} d x = 6 ln ∣ x + 1 ∣

\int \frac{5}{x ^{2} + 9} d x = \frac{5}{3} arctan (\frac{x}{3})

= 6 ln ∣ x + 1 ∣ + \frac{5}{3} arctan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= 6 ln ∣ x + 1 ∣ + \frac{5}{3} arctan (\frac{x}{3}) + C

Graph

Beliebte Beispiele

integral of 2/(x^3sqrt(x^4-1))

\int \frac{2}{x ^{3} x ^{4} - 1} d x

integral of ((8x+1))/(sqrt(4x-3))

\int \frac{( 8 x + 1 )}{4 x - 3} d x

integral of (2-7t)^{2/3}

\int (2 - 7 t)^{\frac{2}{3}} d t

integral of cos(2u-t)

\int cos (2 u - t) d u

integral of y-3

\int y - 3 d y