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Beliebt Rechnen >

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

Lösung

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

Lösung

6 ln ∣ x - 3 ∣ + x + C

Schritte zur Lösung

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

\frac{x + 3}{x - 3} = \frac{6}{x - 3} + 1

= \int \frac{6}{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{6}{x - 3} d x + \int 1 d x

\int \frac{6}{x - 3} d x = 6 ln ∣ x - 3 ∣

\int 1 d x = x

= 6 ln ∣ x - 3 ∣ + x

Füge eine Konstante zur Lösung hinzu

= 6 ln ∣ x - 3 ∣ + x + C

Graph

Beliebte Beispiele

integral of (x^3-3x^2+6x-20)

\int (x^{3} - 3 x^{2} + 6 x - 20) d x

integral of 2y^2x

\int 2 y^{2} x d x

integral of (x^4)/(x^5+3)

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

integral of (e^x+x^3-1/(x^4)+1/(1+x^2))

\int (e^{x} + x^{3} - \frac{1}{x ^{4}} + \frac{1}{1 + x ^{2}}) d x

integral of (11ln(x))/(x^3)

\int \frac{11 ln ( x )}{x ^{3}} d x