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Beliebt Rechnen >

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

Lösung

\int (2 x + 1 - \frac{1}{x + 2}) d x

Lösung

x^{2} + x - ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

\int 2 x d x = x^{2}

\int 1 d x = x

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

= x^{2} + x - ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= x^{2} + x - ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of tan(10x)sec^2(10x)

\int tan (10 x) sec^{2} (10 x) d x

integral of (5x-2)/((x-1)^2(2x+1))

\int \frac{5 x - 2}{( x - 1 ) ^{2} ( 2 x + 1 )} d x

integral of 1/(4xln(x)-3x)

\int \frac{1}{4 x ln ( x ) - 3 x} d x

integral of 1/2 t

\int \frac{1}{2} t d t

integral of (3x+1)^{-2}

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