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(6x^2+x^{1/2})

Lösung

\int x (6 x^{2} + x^{\frac{1}{2}}) d x

Lösung

\frac{3 x ^{4}}{2} + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (6 x^{2} + x^{\frac{1}{2}}) d x

Multipliziere aus

x (6 x^{2} + x^{\frac{1}{2}}) : 6 x^{3} + x^{\frac{3}{2}}

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

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= \frac{3 x ^{4}}{2} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{4}}{2} + \frac{2}{5} x^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

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

integral of 1/(sqrt(-x^2-2x))

integral of ln(x^2+6x+10)

integral of xe^{-0.2x^2}

integral of (2e^x-x^3)