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

Lösung

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

\frac{1}{2} ln (2) x^{2} + \frac{3}{2} ln ∣ x ∣ + C

Schritte zur Lösung

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

\int x ln (2) d x = \frac{1}{2} ln (2) x^{2}

\int \frac{3}{2 x} d x = \frac{3}{2} ln ∣ x ∣

= \frac{1}{2} ln (2) x^{2} + \frac{3}{2} ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln (2) x^{2} + \frac{3}{2} ln ∣ x ∣ + C

d er i v a t i v e f (x) = x - 6

d er i v a t i v e f (x) = 3 e^{2 x^{2}}

\int_{- 2}^{0} (5 x^{2} + 5 x) d x

x \to \infty lim (5 x^{3})

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