de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (11x+2)/(2x^2-5x-3)

Lösung

\int \frac{11 x + 2}{2 x ^{2} - 5 x - 3} d x

Lösung

- \frac{1}{7} (11 x + 2) (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + \frac{11}{14} (2 x (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + ln ∣ 2 x + 1 ∣ + 6 ln ∣ 2 x - 6 ∣) + C

Schritte zur Lösung

\int \frac{11 x + 2}{2 x ^{2} - 5 x - 3} d x

Wende die partielle Integration an

= - \frac{1}{7} (11 x + 2) (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) - \int - \frac{11}{7} (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) d x

\int - \frac{11}{7} (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) d x = - \frac{11}{14} (2 x (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + ln ∣ 2 x + 1 ∣ + 6 ln ∣ 2 x - 6 ∣)

= - \frac{1}{7} (11 x + 2) (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) - (- \frac{11}{14} (2 x (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + ln ∣ 2 x + 1 ∣ + 6 ln ∣ 2 x - 6 ∣))

Vereinfache

- \frac{1}{7} (11 x + 2) (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) - (- \frac{11}{14} (2 x (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + ln ∣ 2 x + 1 ∣ + 6 ln ∣ 2 x - 6 ∣)) : - \frac{1}{7} (11 x + 2) (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + \frac{11}{14} (2 x (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + ln ∣ 2 x + 1 ∣ + 6 ln ∣ 2 x - 6 ∣)

= - \frac{1}{7} (11 x + 2) (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + \frac{11}{14} (2 x (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + ln ∣ 2 x + 1 ∣ + 6 ln ∣ 2 x - 6 ∣)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{7} (11 x + 2) (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + \frac{11}{14} (2 x (ln \frac{2}{7} + \frac{4}{7} x - ln - \frac{12}{7} + \frac{4}{7} x) + ln ∣ 2 x + 1 ∣ + 6 ln ∣ 2 x - 6 ∣) + C

Graph

Beliebte Beispiele

integral of-(sin(2x))/2

\int - \frac{sin ( 2 x )}{2} d x

integral of 3x^2*sqrt(x^3+1)

\int 3 x^{2} \cdot x^{3} + 1 d x

integral of (2x-1)/(x^2-x-6)

\int \frac{2 x - 1}{x ^{2} - x - 6} d x

integral of (4x)/(sqrt(-x^2-8x-7))

\int \frac{4 x}{- x ^{2} - 8 x - 7} d x

integral of xsin(2nx)

\int x sin (2 n x) d x