integral of x/(x+

Lösung

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

- d ln ∣ x + d ∣ + x + C

Schritte zur Lösung

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

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

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

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

\int 1 d x = x

= - d ln ∣ x + d ∣ + x

Füge eine Konstante zur Lösung hinzu

= - d ln ∣ x + d ∣ + x + C

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

y^{^{'''}} = 0

in v erse l a pl a ce \frac{4}{5 s}

\int (6 x + 7 x) d x

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 5