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Beliebt Rechnen >

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

Lösung

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

Lösung

- ln ∣ x + 2 ∣ + x + C

Schritte zur Lösung

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

\frac{x + 1}{x + 2} = - \frac{1}{x + 2} + 1

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

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

\int 1 d x = x

= - ln ∣ x + 2 ∣ + x

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x + 2 ∣ + x + C

Graph

Beliebte Beispiele

integral of x/(sqrt(x+20))

\int \frac{x}{x + 20} d x

(sqrt(x)+x)((dy)/(dx))=sqrt(y)+y

(x + x) (\frac{d y}{d x}) = y + y

tangent f(x)=cos(x),\at (0)

t an g e n t f (x) = cos (x), at (0)

derivative y=((2x+1)(x^3+3))/x

d er i v a t i v e y = \frac{( 2 x + 1 ) ( x ^{3} + 3 )}{x}

tangent 4x^2-2x+3

t an g e n t 4 x^{2} - 2 x + 3