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

Lösung

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

ln ∣ x + 1 ∣ + x + C

Schritte zur Lösung

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

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

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

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

\int 1 d x = x

= ln ∣ x + 1 ∣ + x

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 1 ∣ + x + C

y^{^{'}} (t) = (y + 1) \cdot (y - 3), y (0) = 1

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

x \to 1 lim (x^{2} - 2 x)

\frac{\partial}{\partial y} (x^{2} - 5 x y + 3 y^{2})

\int 4 x^{2} - 16 x + 16 d x