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Beliebt Rechnen >

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

Lösung

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

Lösung

5 ln ∣ x - 3 ∣ + x + C

Schritte zur Lösung

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

\frac{x + 2}{x - 3} = \frac{5}{x - 3} + 1

= \int \frac{5}{x - 3} + 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{5}{x - 3} d x + \int 1 d x

\int \frac{5}{x - 3} d x = 5 ln ∣ x - 3 ∣

\int 1 d x = x

= 5 ln ∣ x - 3 ∣ + x

Füge eine Konstante zur Lösung hinzu

= 5 ln ∣ x - 3 ∣ + x + C

Graph

Beliebte Beispiele

integral of (2^x+x^2)^2

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

integral of (2x^2)/(x-1)

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

integral of (4-5x)^{-3/2}

\int (4 - 5 x)^{- \frac{3}{2}} d x

integral of (2e^x-1)/(e^x-1)

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

integral of (x^2)/(sqrt(x^2-81))

\int \frac{x ^{2}}{x ^{2} - 81} d x