de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

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

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of y(4+y^2)

\int y (4 + y^{2}) d y

integral of (2x-9)/(sqrt(x^2-9x+5))

\int \frac{2 x - 9}{x ^{2} - 9 x + 5} d x

integral of 2sin^5(x)cos^4(x)

\int 2 sin^{5} (x) cos^{4} (x) d x

integral of 1/2 cot^3(x)csc(x)

\int \frac{1}{2} cot^{3} (x) csc (x) d x

integral of x^3(x^2+4)^{1/2}

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