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Beliebt Rechnen >

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

Lösung

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

Lösung

2 x^{2} - 4 x + 9 ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

Lange Division

\frac{( 2 x + 1 ) ^{2}}{x + 2} : 4 x - 4 + \frac{9}{x + 2}

= \int 4 x - 4 + \frac{9}{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 4 x d x - \int 4 d x + \int \frac{9}{x + 2} d x

\int 4 x d x = 2 x^{2}

\int 4 d x = 4 x

\int \frac{9}{x + 2} d x = 9 ln ∣ x + 2 ∣

= 2 x^{2} - 4 x + 9 ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= 2 x^{2} - 4 x + 9 ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of 5sec(x)tan(x)

\int 5 sec (x) tan (x) d x

(\partial)/(\partial x)(-2x^2y-y)

\frac{\partial}{\partial x} (- 2 x^{2} y - y)

integral of-sin(x)+cos(x)

\int - sin (x) + cos (x) d x

integral of 1/(sqrt(x^2+625))

\int \frac{1}{x ^{2} + 625} d x

limit as x approaches 0 of (|x|)/(x^3-5)

x \to 0 lim (\frac{∣ x ∣}{x ^{3} - 5})