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Beliebt Rechnen >

integral of (4x+3)/(2x+1)

Lösung

\int \frac{4 x + 3}{2 x + 1} d x

Lösung

2 x + \frac{1}{2} ln ∣ 2 x + 1 ∣ + C

Schritte zur Lösung

\int \frac{4 x + 3}{2 x + 1} d x

Lange Division

\frac{4 x + 3}{2 x + 1} : 2 + \frac{1}{2 x + 1}

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

\int 2 d x = 2 x

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

= 2 x + \frac{1}{2} ln ∣ 2 x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 2 x + \frac{1}{2} ln ∣ 2 x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of r^{-2}

\int r^{- 2} d r

integral of x^2+2x-3

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

integral of sqrt((x^2+4))

\int (x^{2} + 4) d x

limit as θ approaches 0 of (sin(θ))/(sin(2θ))

θ \to 0 lim (\frac{sin ( θ )}{sin ( 2 θ )})

(\partial)/(\partial x)(5xcos(x)cos(y))

\frac{\partial}{\partial x} (5 x cos (x) cos (y))