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(9-x^2)^{1/5}

Lösung

\int x^{3} (9 - x^{2})^{\frac{1}{5}} d x

Lösung

- \frac{1}{2} (- \frac{5}{11} (9 - x^{2})^{\frac{11}{5}} + \frac{15}{2} (9 - x^{2})^{\frac{6}{5}}) + C

Schritte zur Lösung

\int x^{3} (9 - x^{2})^{\frac{1}{5}} d x

Wende U-Substitution an

= \int - \frac{( - u + 9 ) u ^{\frac{1}{5}}}{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 + 9) u^{\frac{1}{5}} d u

Multipliziere aus

(- u + 9) u^{\frac{1}{5}} : - u^{\frac{6}{5}} + 9 u^{\frac{1}{5}}

= - \frac{1}{2} \cdot \int - u^{\frac{6}{5}} + 9 u^{\frac{1}{5}} 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}{2} (- \int u^{\frac{6}{5}} d u + \int 9 u^{\frac{1}{5}} d u)

\int u^{\frac{6}{5}} d u = \frac{5}{11} u^{\frac{11}{5}}

\int 9 u^{\frac{1}{5}} d u = \frac{15}{2} u^{\frac{6}{5}}

= - \frac{1}{2} (- \frac{5}{11} u^{\frac{11}{5}} + \frac{15}{2} u^{\frac{6}{5}})

Setze in

u = 9 - x^{2}

ein

= - \frac{1}{2} (- \frac{5}{11} (9 - x^{2})^{\frac{11}{5}} + \frac{15}{2} (9 - x^{2})^{\frac{6}{5}})

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} (- \frac{5}{11} (9 - x^{2})^{\frac{11}{5}} + \frac{15}{2} (9 - x^{2})^{\frac{6}{5}}) + C

Graph

Beliebte Beispiele

integral of 1/(xsqrt(100x^2-1))

\int \frac{1}{x 100 x ^{2} - 1} d x

integral of 7cos(5x)

\int 7 cos (5 x) d x

integral of ((4x-3))/(x^2+7x+12)

\int \frac{( 4 x - 3 )}{x ^{2} + 7 x + 12} d x

integral of 3x(6x^2+1)^3

\int 3 x (6 x^{2} + 1)^{3} d x

integral of 1/(xyz)

\int \frac{1}{x yz} d x