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^{3/2}-x^{1/3})/(6x^{1/4)}

Lösung

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

Lösung

\frac{2}{351} (- 27 x^{\frac{13}{12}} + 13 x^{\frac{9}{4}}) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

\frac{x ^{\frac{3}{2}} - x ^{\frac{1}{3}}}{x ^{\frac{1}{4}}} : x^{\frac{5}{4}} - x^{\frac{1}{12}}

= \frac{1}{6} \cdot \int x^{\frac{5}{4}} - x^{\frac{1}{12}} 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}{6} (\int x^{\frac{5}{4}} d x - \int x^{\frac{1}{12}} d x)

\int x^{\frac{5}{4}} d x = \frac{4}{9} x^{\frac{9}{4}}

\int x^{\frac{1}{12}} d x = \frac{12}{13} x^{\frac{13}{12}}

= \frac{1}{6} (\frac{4}{9} x^{\frac{9}{4}} - \frac{12}{13} x^{\frac{13}{12}})

Vereinfache

\frac{1}{6} (\frac{4}{9} x^{\frac{9}{4}} - \frac{12}{13} x^{\frac{13}{12}}) : \frac{2}{351} (- 27 x^{\frac{13}{12}} + 13 x^{\frac{9}{4}})

= \frac{2}{351} (- 27 x^{\frac{13}{12}} + 13 x^{\frac{9}{4}})

Füge eine Konstante zur Lösung hinzu

= \frac{2}{351} (- 27 x^{\frac{13}{12}} + 13 x^{\frac{9}{4}}) + C

Graph

Beliebte Beispiele

integral of (\sqrt[9]{x^2}-3/(x^2))

\int (9 x^{2} - \frac{3}{x ^{2}}) d x

integral of e^{ln(3cos(x))}

\int e^{l n (3 c o s (x))} d x

integral of 3/(sqrt(1+9y^2))

\int \frac{3}{1 + 9 y ^{2}} d y

integral of 500-x/3

\int 500 - \frac{x}{3} d x

integral of (-x)/2

\int \frac{- x}{2} d x