integral of ((2x+7))/(x+3)

Lösung

\int \frac{( 2 x + 7 )}{x + 3} d x

2 (x + 3) + ln ∣ x + 3 ∣ + C

Schritte zur Lösung

\int \frac{2 x + 7}{x + 3} d x

Wende U-Substitution an

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

Multipliziere aus

\frac{2 u + 1}{u} : 2 + \frac{1}{u}

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

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 u + \int \frac{1}{u} d u

\int 2 d u = 2 u

\int \frac{1}{u} d u = ln ∣ u ∣

= 2 u + ln ∣ u ∣

Setze in

u = x + 3

ein

= 2 (x + 3) + ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= 2 (x + 3) + ln ∣ x + 3 ∣ + C

\int (x + 4) sin (nπ x) d x

n = 1 \sum \infty 8 (\frac{1}{4})^{n}

\frac{\partial}{\partial x} (r cos (x) sin (y))

\frac{d y}{d t} = k y (1 - \frac{y}{4600})

a re a f (x) = 8 sin (x), g (x) = 8 cos (2 x)