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

Lösung

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

Lösung

\frac{x ^{3}}{3} + 3 x + \frac{1}{x ^{2}} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int 3 d x = 3 x

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

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

Vereinfache

= \frac{x ^{3}}{3} + 3 x + \frac{1}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + 3 x + \frac{1}{x ^{2}} + C

Graph

Beliebte Beispiele

2x(1+y^2)dx-y(1+2x^2)dy=0

2 x (1 + y^{2}) d x - y (1 + 2 x^{2}) d y = 0

integral of 1/(x^4+1)

\int \frac{1}{x ^{4} + 1} d x

limit as x approaches-2 of e^{x+x^2}

x \to - 2 lim (e^{x + x^{2}})

limit as x approaches 0 of x^3(x^4+2x^3)

x \to 0 lim (x^{3} (x^{4} + 2 x^{3}))

integral of (e^x)/(6e^x+2)

\int \frac{e ^{x}}{6 e ^{x} + 2} d x