de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/(2x^2+5x+2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{2 x ^{2} + 5 x + 2} : \frac{2}{3 ( 2 x + 1 )} - \frac{1}{3 ( x + 2 )}

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

\int \frac{2}{3 ( 2 x + 1 )} d x = \frac{1}{3} ln ∣ 2 x + 1 ∣

\int \frac{1}{3 ( x + 2 )} d x = \frac{1}{3} ln ∣ x + 2 ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of sin(7x)sin(2x)

\int sin (7 x) sin (2 x) d x

integral of sin^2(1/3 θ)

\int sin^{2} (\frac{1}{3} θ) d θ

integral of 1/(2x^2+5x+3)

\int \frac{1}{2 x ^{2} + 5 x + 3} d x

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

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

integral of 84x^{-1/5}tan(x^{4/5})

\int 84 x^{- \frac{1}{5}} tan (x^{\frac{4}{5}}) d x