de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (6x^3+4x^2-2x)/(2x^2)

Lösung

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

Lösung

\frac{3}{2} x^{2} + 2 x - ln ∣ x ∣ + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{6 x ^{3} + 4 x ^{2} - 2 x}{x ^{2}} d x

Multipliziere aus

\frac{6 x ^{3} + 4 x ^{2} - 2 x}{x ^{2}} : 6 x + 4 - \frac{2}{x}

= \frac{1}{2} \cdot \int 6 x + 4 - \frac{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

= \frac{1}{2} (\int 6 x d x + \int 4 d x - \int \frac{2}{x} d x)

\int 6 x d x = 3 x^{2}

\int 4 d x = 4 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{1}{2} (3 x^{2} + 4 x - 2 ln ∣ x ∣)

Vereinfache

\frac{1}{2} (3 x^{2} + 4 x - 2 ln ∣ x ∣) : \frac{3}{2} x^{2} + 2 x - ln ∣ x ∣

= \frac{3}{2} x^{2} + 2 x - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} x^{2} + 2 x - ln ∣ x ∣ + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(x^3-xsin(y))

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

integral from-1 to 0 of x^3-x

\int_{- 1}^{0} x^{3} - x d x

limit as x approaches 2 of (5x)/(x-2)

x \to 2 lim (\frac{5 x}{x - 2})

integral of e^{2θ}sin(3θ)

\int e^{2 θ} sin (3 θ) d θ

(ln (f (x)))^{'}