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Beliebt Rechnen >

integral of 3/y-1/(y+3)

Lösung

\int \frac{3}{y} - \frac{1}{y + 3} d y

Lösung

3 ln ∣ y ∣ - ln ∣ y + 3 ∣ + C

Schritte zur Lösung

\int \frac{3}{y} - \frac{1}{y + 3} d y

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{3}{y} d y - \int \frac{1}{y + 3} d y

\int \frac{3}{y} d y = 3 ln ∣ y ∣

\int \frac{1}{y + 3} d y = ln ∣ y + 3 ∣

= 3 ln ∣ y ∣ - ln ∣ y + 3 ∣

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ y ∣ - ln ∣ y + 3 ∣ + C

Graph

Beliebte Beispiele

derivative of e^ysin(x)

\frac{d}{d x} (e^{y} sin (x))

integral of 3/(xsqrt(1+2x))

\int \frac{3}{x 1 + 2 x} d x

integral of 5x(sin(x))

\int 5 x (sin (x)) d x

derivative of 2sec(x+cot(x))

\frac{d}{d x} (2 sec (x) + cot (x))

integral of (x+1)/x

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