de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (24s+24)/((s^2+1)(s-1)^3)

Lösung

\int \frac{24 s + 24}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

Lösung

12 arctan (s) + \frac{12}{s - 1} - \frac{12}{( s - 1 ) ^{2}} + C

Schritte zur Lösung

\int \frac{24 s + 24}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

Ermittle den Partialbruch von

\frac{24 s + 24}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} : \frac{12}{s ^{2} + 1} - \frac{12}{( s - 1 ) ^{2}} + \frac{24}{( s - 1 ) ^{3}}

= \int \frac{12}{s ^{2} + 1} - \frac{12}{( s - 1 ) ^{2}} + \frac{24}{( s - 1 ) ^{3}} d s

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{12}{s ^{2} + 1} d s - \int \frac{12}{( s - 1 ) ^{2}} d s + \int \frac{24}{( s - 1 ) ^{3}} d s

\int \frac{12}{s ^{2} + 1} d s = 12 arctan (s)

\int \frac{12}{( s - 1 ) ^{2}} d s = - \frac{12}{s - 1}

\int \frac{24}{( s - 1 ) ^{3}} d s = - \frac{12}{( s - 1 ) ^{2}}

= 12 arctan (s) - (- \frac{12}{s - 1}) - \frac{12}{( s - 1 ) ^{2}}

Vereinfache

= 12 arctan (s) + \frac{12}{s - 1} - \frac{12}{( s - 1 ) ^{2}}

Füge eine Konstante zur Lösung hinzu

= 12 arctan (s) + \frac{12}{s - 1} - \frac{12}{( s - 1 ) ^{2}} + C

Graph

Beliebte Beispiele

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

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

integral of sqrt(1+((x^6-1)^2)/(4x^6))

\int 1 + \frac{( x ^{6} - 1 ) ^{2}}{4 x ^{6}} d x

integral of x/(1+4x^4)

\int \frac{x}{1 + 4 x ^{4}} d x

integral of 1/(2+e^x+e^{-x)}

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

integral of (4e^{-2t}+4)

\int (4 e^{- 2 t} + 4) d t