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Beliebt Rechnen >

integral of (5x+3)/(x^2+x)

Lösung

\int \frac{5 x + 3}{x ^{2} + x} d x

Lösung

3 ln ∣ x ∣ + 2 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{5 x + 3}{x ^{2} + x} d x

Ermittle den Partialbruch von

\frac{5 x + 3}{x ^{2} + x} : \frac{3}{x} + \frac{2}{x + 1}

= \int \frac{3}{x} + \frac{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{3}{x} d x + \int \frac{2}{x + 1} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{2}{x + 1} d x = 2 ln ∣ x + 1 ∣

= 3 ln ∣ x ∣ + 2 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x ∣ + 2 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of (-36)/(x^2sqrt(9-x^2))

\int \frac{- 36}{x ^{2} 9 - x ^{2}} d x

integral of 1/(v^4)

\int \frac{1}{v ^{4}} d v

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\int \frac{( y ^{2} - 14 y + 5 )}{y ( y - 1 ) ( y - 5 )} d y

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

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

integral of 7x+14xln(3x)

\int 7 x + 14 x ln (3 x) d x