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(\sqrt[3]{1-4x})

Lösung

\int x (3 1 - 4 x) d x

Lösung

\frac{1}{16} (\frac{3}{7} (1 - 4 x)^{\frac{7}{3}} - \frac{3}{4} (1 - 4 x)^{\frac{4}{3}}) + C

Schritte zur Lösung

\int x 3 1 - 4 x d x

Wende U-Substitution an

= \int \frac{3 u ( u - 1 )}{16} d u

Entferne die Konstante:

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

= \frac{1}{16} \cdot \int 3 u (u - 1) d u

Multipliziere aus

3 u (u - 1) : u^{\frac{4}{3}} - 3 u

= \frac{1}{16} \cdot \int u^{\frac{4}{3}} - 3 u d u

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}{16} (\int u^{\frac{4}{3}} d u - \int 3 u d u)

\int u^{\frac{4}{3}} d u = \frac{3}{7} u^{\frac{7}{3}}

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

= \frac{1}{16} (\frac{3}{7} u^{\frac{7}{3}} - \frac{3}{4} u^{\frac{4}{3}})

Setze in

u = 1 - 4 x

ein

= \frac{1}{16} (\frac{3}{7} (1 - 4 x)^{\frac{7}{3}} - \frac{3}{4} (1 - 4 x)^{\frac{4}{3}})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{16} (\frac{3}{7} (1 - 4 x)^{\frac{7}{3}} - \frac{3}{4} (1 - 4 x)^{\frac{4}{3}}) + C

Graph

Beliebte Beispiele

integral of 3x^{-6/7}

\int 3 x^{- \frac{6}{7}} d x

integral of sqrt(3-4x)

\int 3 - 4 x d x

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

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

integral of 1/3*x^3cos(x^4+2)

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

integral of 7cos(x)tan(x)

\int 7 cos (x) tan (x) d x