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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x ∣ - 3 arctan (x) + C

Schritte zur Lösung

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{3}{x ^{2} + 1} d x = 3 arctan (x)

= ln ∣ x ∣ - 3 arctan (x)

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - 3 arctan (x) + C

Graph

Beliebte Beispiele

integral of (2sin(x))

\int (2 sin (x)) d x

derivative of (3x^3/2)

\frac{d}{d x} (\frac{3 x ^{3}}{2})

(ye^{xy}cos(2x)-2e^{xy}sin(2x)+2x)+(xe^{xy}cos(2x)-3)y^'=0

(y e^{x y} cos (2 x) - 2 e^{x y} sin (2 x) + 2 x) + (x e^{x y} cos (2 x) - 3) y^{^{'}} = 0

limit as x approaches 0 of (1-6x)^{5/x}

x \to 0 lim ((1 - 6 x)^{\frac{5}{x}})

(dy)/(dx)-sin(x)y=2sin(x)

\frac{d y}{d x} - sin (x) y = 2 sin (x)