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[4]{(x^2-1)^3}

Lösung

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

Lösung

\frac{2}{7} (x^{2} - 1)^{\frac{7}{4}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u ^{\frac{3}{4}}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int u^{\frac{3}{4}} d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{4}{7} u^{\frac{7}{4}}

Setze in

u = x^{2} - 1

ein

= \frac{1}{2} \cdot \frac{4}{7} (x^{2} - 1)^{\frac{7}{4}}

Vereinfache

\frac{1}{2} \cdot \frac{4}{7} (x^{2} - 1)^{\frac{7}{4}} : \frac{2}{7} (x^{2} - 1)^{\frac{7}{4}}

= \frac{2}{7} (x^{2} - 1)^{\frac{7}{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} (x^{2} - 1)^{\frac{7}{4}} + C

Graph

Beliebte Beispiele

integral of rctan(sqrt(x))

\int d arctan (x) d x

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

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

integral of (ax+b)^{3/2}

\int (a x + b)^{\frac{3}{2}} d x

integral of 1/(5x-x^2)

\int \frac{1}{5 x - x ^{2}} d x

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

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