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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x + 2 ∣ + x + C

Schritte zur Lösung

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

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

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

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

\int 1 d x = x

= ln ∣ x + 2 ∣ + x

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 2 ∣ + x + C

Graph

Beliebte Beispiele

integral of 1/(x^2-10x+32)

\int \frac{1}{x ^{2} - 10 x + 32} d x

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\int sec^{2} (x) \cdot tan (x) d x

integral of (6x)/((x^2-6)^5)

\int \frac{6 x}{( x ^{2} - 6 ) ^{5}} d x

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\int 36 (1 + x^{2}) (7 + 12 x + 4 x^{3})^{10} d x

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\int e^{x} (x + sin (e^{x})) d x