de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (z^2+2z+3)/((z-6)(z^2+4))

Lösung

\int \frac{z ^{2} + 2 z + 3}{( z - 6 ) ( z ^{2} + 4 )} d z

Lösung

\frac{51}{40} ln ∣ z - 6 ∣ + \frac{1}{40} (- \frac{11}{2} ln z^{2} + 4 + 7 arctan (\frac{z}{2})) + C

Schritte zur Lösung

\int \frac{z ^{2} + 2 z + 3}{( z - 6 ) ( z ^{2} + 4 )} d z

Ermittle den Partialbruch von

\frac{z ^{2} + 2 z + 3}{( z - 6 ) ( z ^{2} + 4 )} : \frac{51}{40 ( z - 6 )} + \frac{- 11 z + 14}{40 ( z ^{2} + 4 )}

= \int \frac{51}{40 ( z - 6 )} + \frac{- 11 z + 14}{40 ( z ^{2} + 4 )} d z

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{51}{40 ( z - 6 )} d z + \int \frac{- 11 z + 14}{40 ( z ^{2} + 4 )} d z

\int \frac{51}{40 ( z - 6 )} d z = \frac{51}{40} ln ∣ z - 6 ∣

\int \frac{- 11 z + 14}{40 ( z ^{2} + 4 )} d z = \frac{1}{40} (- \frac{11}{2} ln z^{2} + 4 + 7 arctan (\frac{z}{2}))

= \frac{51}{40} ln ∣ z - 6 ∣ + \frac{1}{40} (- \frac{11}{2} ln z^{2} + 4 + 7 arctan (\frac{z}{2}))

Füge eine Konstante zur Lösung hinzu

= \frac{51}{40} ln ∣ z - 6 ∣ + \frac{1}{40} (- \frac{11}{2} ln z^{2} + 4 + 7 arctan (\frac{z}{2})) + C

Graph

Beliebte Beispiele

integral of 20x^3(5x^4-1)^3

\int 20 x^{3} (5 x^{4} - 1)^{3} d x

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

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

integral of ((2x+2))/(x^2+10x+24)

\int \frac{( 2 x + 2 )}{x ^{2} + 10 x + 24} d x

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

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

integral of ln(x)\sqrt[3]{x}

\int ln (x) 3 x d x