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Beliebt Rechnen >

integral of (x+9)/(x-9)-(y+21)/(y+39)

Lösung

\int \frac{x + 9}{x - 9} - \frac{y + 21}{y + 39}

Lösung

- \frac{21 + y}{39 + y} x + 18 ln ∣ - 9 + x ∣ + x + C

Schritte zur Lösung

\int \frac{x + 9}{x - 9} - \frac{y + 21}{y + 39} 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{21 + y}{39 + y} d x + \int \frac{9 + x}{- 9 + x} d x

\int \frac{21 + y}{39 + y} d x = \frac{21 + y}{39 + y} x

\int \frac{9 + x}{- 9 + x} d x = 18 ln ∣ - 9 + x ∣ + x

= - \frac{21 + y}{39 + y} x + 18 ln ∣ - 9 + x ∣ + x

Füge eine Konstante zur Lösung hinzu

= - \frac{21 + y}{39 + y} x + 18 ln ∣ - 9 + x ∣ + x + C

Graph

Beliebte Beispiele

integral of 9x^8-8/(x^8)

\int 9 x^{8} - \frac{8}{x ^{8}} d x

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\int \frac{1}{e ^{2 x} + 9} d x

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

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\int \frac{2 e ^{x}}{e ^{x} - 1} d x

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