de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

- ln ∣ 2 x + 1 ∣ + 2 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

= ln ∣ 2 x + 1 ∣ + 2 (ln ∣ x ∣ - ln ∣ 2 x + 1 ∣)

Vereinfache

ln ∣ 2 x + 1 ∣ + 2 (ln ∣ x ∣ - ln ∣ 2 x + 1 ∣) : - ln ∣ 2 x + 1 ∣ + 2 ln ∣ x ∣

= - ln ∣ 2 x + 1 ∣ + 2 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ 2 x + 1 ∣ + 2 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of 4/(xsqrt(x^2-36))

\int \frac{4}{x x ^{2} - 36} d x

integral of 1/(yIn^2y)

\int \frac{1}{y I n ^{2} y} d y

integral of x^3(2-x^2)

\int x^{3} (2 - x^{2}) d x

integral of (x^2)/(sqrt(10x-x^2))

\int \frac{x ^{2}}{10 x - x ^{2}} d x

integral of 5x^2+sqrt(x)

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