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Beliebt Rechnen >

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

Lösung

\int \frac{5}{( x - 3 ) ( 2 x + 5 )} d x

Lösung

5 (\frac{1}{11} ln ∣ x - 3 ∣ - \frac{1}{11} ln ∣ 2 x + 5 ∣) + C

Schritte zur Lösung

\int \frac{5}{( x - 3 ) ( 2 x + 5 )} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{1}{( x - 3 ) ( 2 x + 5 )} d x

Ermittle den Partialbruch von

\frac{1}{( x - 3 ) ( 2 x + 5 )} : \frac{1}{11 ( x - 3 )} - \frac{2}{11 ( 2 x + 5 )}

= 5 \cdot \int \frac{1}{11 ( x - 3 )} - \frac{2}{11 ( 2 x + 5 )} 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

= 5 (\int \frac{1}{11 ( x - 3 )} d x - \int \frac{2}{11 ( 2 x + 5 )} d x)

\int \frac{1}{11 ( x - 3 )} d x = \frac{1}{11} ln ∣ x - 3 ∣

\int \frac{2}{11 ( 2 x + 5 )} d x = \frac{1}{11} ln ∣ 2 x + 5 ∣

= 5 (\frac{1}{11} ln ∣ x - 3 ∣ - \frac{1}{11} ln ∣ 2 x + 5 ∣)

Füge eine Konstante zur Lösung hinzu

= 5 (\frac{1}{11} ln ∣ x - 3 ∣ - \frac{1}{11} ln ∣ 2 x + 5 ∣) + C

Graph

Beliebte Beispiele

integral of (x+sqrt(1-x^2))^2

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

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

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\int e^{x} (2 + 3 e^{x})^{4} d x

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\int x^{3} (x^{2} + 1)^{13} d x

integral of (ln^7(z))/z

\int \frac{ln ^{7} ( z )}{z} d z