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+3)/(x+2)

Lösung

\int \frac{x ^{2} + x + 3}{x + 2} d x

Lösung

- 3 x + 5 ln ∣ x + 2 ∣ + \frac{1}{2} (x + 2)^{2} - 6 + C

Schritte zur Lösung

\int \frac{x ^{2} + x + 3}{x + 2} d x

Multipliziere aus

\frac{x ^{2} + x + 3}{x + 2} : \frac{x ^{2}}{x + 2} + \frac{x}{x + 2} + \frac{3}{x + 2}

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{x ^{2}}{x + 2} d x + \int \frac{x}{x + 2} d x + \int \frac{3}{x + 2} d x

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

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

\int \frac{3}{x + 2} d x = 3 ln ∣ x + 2 ∣

= \frac{( x + 2 ) ^{2}}{2} - 4 (x + 2) + 4 ln ∣ x + 2 ∣ + x + 2 - 2 ln ∣ x + 2 ∣ + 3 ln ∣ x + 2 ∣

Vereinfache

\frac{( x + 2 ) ^{2}}{2} - 4 (x + 2) + 4 ln ∣ x + 2 ∣ + x + 2 - 2 ln ∣ x + 2 ∣ + 3 ln ∣ x + 2 ∣ : - 3 x + 5 ln ∣ x + 2 ∣ + \frac{1}{2} (x + 2)^{2} - 6

= - 3 x + 5 ln ∣ x + 2 ∣ + \frac{1}{2} (x + 2)^{2} - 6

Füge eine Konstante zur Lösung hinzu

= - 3 x + 5 ln ∣ x + 2 ∣ + \frac{1}{2} (x + 2)^{2} - 6 + C

Graph

Beliebte Beispiele

integral of 5x^3sqrt(x^2+2)

\int 5 x^{3} x^{2} + 2 d x

integral of-3(t+2)^{-2}

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

integral of 5/(x(x^2+6)^2)

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

integral of ((y-3))/(y^2-6y+1)

\int \frac{( y - 3 )}{y ^{2} - 6 y + 1} d y

integral of cos^6(x/2)sin^4(x/2)

\int cos^{6} (\frac{x}{2}) sin^{4} (\frac{x}{2}) d x