de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{5}{7} ln ∣ 2 x - 1 ∣ + \frac{19}{14} ln 4 x^{2} + 4 x + 4 - \frac{11}{7 3} arctan (\frac{1}{3} (2 x + 1)) + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{4 x ^{2} - 3 x - 2}{2 x ^{3} + x ^{2} + x - 1} : - \frac{10}{7 ( 2 x - 1 )} + \frac{19 x + 4}{7 ( x ^{2} + x + 1 )}

= \int - \frac{10}{7 ( 2 x - 1 )} + \frac{19 x + 4}{7 ( x ^{2} + x + 1 )} 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{10}{7 ( 2 x - 1 )} d x + \int \frac{19 x + 4}{7 ( x ^{2} + x + 1 )} d x

\int \frac{10}{7 ( 2 x - 1 )} d x = \frac{5}{7} ln ∣ 2 x - 1 ∣

\int \frac{19 x + 4}{7 ( x ^{2} + x + 1 )} d x = \frac{1}{14 3} (193 ln 4 x^{2} + 4 x + 4 - 22 arctan (\frac{2 x + 1}{3}))

= - \frac{5}{7} ln ∣ 2 x - 1 ∣ + \frac{1}{14 3} (193 ln 4 x^{2} + 4 x + 4 - 22 arctan (\frac{2 x + 1}{3}))

Vereinfache

- \frac{5}{7} ln ∣ 2 x - 1 ∣ + \frac{1}{14 3} (193 ln 4 x^{2} + 4 x + 4 - 22 arctan (\frac{2 x + 1}{3})) : - \frac{5}{7} ln ∣ 2 x - 1 ∣ + \frac{19}{14} ln 4 x^{2} + 4 x + 4 - \frac{11}{7 3} arctan (\frac{1}{3} (2 x + 1))

= - \frac{5}{7} ln ∣ 2 x - 1 ∣ + \frac{19}{14} ln 4 x^{2} + 4 x + 4 - \frac{11}{7 3} arctan (\frac{1}{3} (2 x + 1))

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{7} ln ∣ 2 x - 1 ∣ + \frac{19}{14} ln 4 x^{2} + 4 x + 4 - \frac{11}{7 3} arctan (\frac{1}{3} (2 x + 1)) + C

Graph

Beliebte Beispiele

integral of-40sin(5y+1)

\int - 40 sin (5 y + 1) d y

integral of cos(sqrt(x+2))

\int cos (x + 2) d x

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

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

integral of (3x^2-x+1)

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

integral of (cos(t))/(8+sin(t))

\int \frac{cos ( t )}{8 + sin ( t )} d t