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Beliebt Rechnen >

integral of (x-28)/(x^2(x+4))

Lösung

\int \frac{x - 28}{x ^{2} ( x + 4 )} d x

Lösung

2 ln ∣ x ∣ + \frac{7}{x} - 2 ln ∣ x + 4 ∣ + C

Schritte zur Lösung

\int \frac{x - 28}{x ^{2} ( x + 4 )} d x

Ermittle den Partialbruch von

\frac{x - 28}{x ^{2} ( x + 4 )} : \frac{2}{x} - \frac{7}{x ^{2}} - \frac{2}{x + 4}

= \int \frac{2}{x} - \frac{7}{x ^{2}} - \frac{2}{x + 4} 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{2}{x} d x - \int \frac{7}{x ^{2}} d x - \int \frac{2}{x + 4} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{7}{x ^{2}} d x = - \frac{7}{x}

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

= 2 ln ∣ x ∣ - (- \frac{7}{x}) - 2 ln ∣ x + 4 ∣

Vereinfache

= 2 ln ∣ x ∣ + \frac{7}{x} - 2 ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + \frac{7}{x} - 2 ln ∣ x + 4 ∣ + C

Graph

Beliebte Beispiele

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\int \frac{6 x ^{2}}{x ^{4} - 5 x ^{2} + 4} d x

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\int 22 tan^{6} (x) d x

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\int \frac{7}{4} d x

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