integral of (2/x+3sin(x)-4e^x)

Lösung

\int (\frac{2}{x} + 3 sin (x) - 4 e^{x}) d x

2 ln ∣ x ∣ - 3 cos (x) - 4 e^{x} + C

Schritte zur Lösung

\int \frac{2}{x} + 3 sin (x) - 4 e^{x} 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{2}{x} d x + \int 3 sin (x) d x - \int 4 e^{x} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 3 sin (x) d x = - 3 cos (x)

\int 4 e^{x} d x = 4 e^{x}

= 2 ln ∣ x ∣ - 3 cos (x) - 4 e^{x}

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ - 3 cos (x) - 4 e^{x} + C

a re a y = 1 + 3 x, 1 \leq x \leq 9

x \to \infty lim (a^{x})

\int_{3}^{4} \frac{2 x - 3}{6} d x

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

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