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

Lösung

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

- ln ∣ x + 3 ∣ + x + C

Schritte zur Lösung

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

\frac{x + 2}{x + 3} = - \frac{1}{x + 3} + 1

= \int - \frac{1}{x + 3} + 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 + 3} d x + \int 1 d x

\int \frac{1}{x + 3} d x = ln ∣ x + 3 ∣

\int 1 d x = x

= - ln ∣ x + 3 ∣ + x

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x + 3 ∣ + x + C

- 10 x^{2} y + y^{^{'}} = 9 x^{2}

\int \frac{1}{3 ^{x} + 1} d x

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = - 3, y^{^{'}} (0) = 5

\int_{1}^{3} (x + 2) (x - 1)^{5} d x

\frac{d}{d x} (\frac{- x ^{2} - 4 x - 1}{4 x - 3})