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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{15}{4} ln ∣ x ∣ + \frac{11}{2 x} - \frac{15}{4} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{2 x - 11}{x ^{3} + 2 x ^{2}} : \frac{15}{4 x} - \frac{11}{2 x ^{2}} - \frac{15}{4 ( x + 2 )}

= \int \frac{15}{4 x} - \frac{11}{2 x ^{2}} - \frac{15}{4 ( x + 2 )} 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{15}{4 x} d x - \int \frac{11}{2 x ^{2}} d x - \int \frac{15}{4 ( x + 2 )} d x

\int \frac{15}{4 x} d x = \frac{15}{4} ln ∣ x ∣

\int \frac{11}{2 x ^{2}} d x = - \frac{11}{2 x}

\int \frac{15}{4 ( x + 2 )} d x = \frac{15}{4} ln ∣ x + 2 ∣

= \frac{15}{4} ln ∣ x ∣ - (- \frac{11}{2 x}) - \frac{15}{4} ln ∣ x + 2 ∣

Vereinfache

= \frac{15}{4} ln ∣ x ∣ + \frac{11}{2 x} - \frac{15}{4} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{15}{4} ln ∣ x ∣ + \frac{11}{2 x} - \frac{15}{4} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of 1/(sqrt(1-3x))

\int \frac{1}{1 - 3 x} d x

integral of sqrt(1-9t^2)

\int 1 - 9 t^{2} d t

integral of (x+3)sqrt(x-1)

\int (x + 3) x - 1 d x

integral of ((x^9))/(1+x^{20)}

\int \frac{( x ^{9} )}{1 + x ^{20}} d x

in t e g r a l x e^{x}