de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (10s+10)/((s^2+1)(s-1)^3)

Lösung

\int \frac{10 s + 10}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

Lösung

5 arctan (s) + \frac{5}{s - 1} - \frac{5}{( s - 1 ) ^{2}} + C

Schritte zur Lösung

\int \frac{10 s + 10}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

Ermittle den Partialbruch von

\frac{10 s + 10}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} : \frac{5}{s ^{2} + 1} - \frac{5}{( s - 1 ) ^{2}} + \frac{10}{( s - 1 ) ^{3}}

= \int \frac{5}{s ^{2} + 1} - \frac{5}{( s - 1 ) ^{2}} + \frac{10}{( 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{5}{s ^{2} + 1} d s - \int \frac{5}{( s - 1 ) ^{2}} d s + \int \frac{10}{( s - 1 ) ^{3}} d s

\int \frac{5}{s ^{2} + 1} d s = 5 arctan (s)

\int \frac{5}{( s - 1 ) ^{2}} d s = - \frac{5}{s - 1}

\int \frac{10}{( s - 1 ) ^{3}} d s = - \frac{5}{( s - 1 ) ^{2}}

= 5 arctan (s) - (- \frac{5}{s - 1}) - \frac{5}{( s - 1 ) ^{2}}

Vereinfache

= 5 arctan (s) + \frac{5}{s - 1} - \frac{5}{( s - 1 ) ^{2}}

Füge eine Konstante zur Lösung hinzu

= 5 arctan (s) + \frac{5}{s - 1} - \frac{5}{( s - 1 ) ^{2}} + C

Graph

Beliebte Beispiele

in t e g r a l x - 1

integral of (x^2-x^5+sqrt(x))/(x^5)

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

integral of cos^5(3x)sin^3(3x)

\int cos^{5} (3 x) sin^{3} (3 x) d x

integral of e^{-3x}-3x

\int e^{- 3 x} - 3 x d x

integral of 1/((4x+5)^3)

\int \frac{1}{( 4 x + 5 ) ^{3}} d x