de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((sqrt(4-x^2))^3)/3

Lösung

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

Lösung

\frac{1}{3} (x (4 - x^{2})^{\frac{3}{2}} + 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x)))) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int - 3 x^{2} 4 - x^{2} d x = - 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x)))

= \frac{1}{3} (x (4 - x^{2})^{3} - (- 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x)))))

Vereinfache

\frac{1}{3} (x (4 - x^{2})^{3} - (- 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x))))) : \frac{1}{3} (x (4 - x^{2})^{\frac{3}{2}} + 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x))))

= \frac{1}{3} (x (4 - x^{2})^{\frac{3}{2}} + 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x))))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (x (4 - x^{2})^{\frac{3}{2}} + 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x)))) + C

Graph

Beliebte Beispiele

integral of 6xcos(7x)

\int 6 x cos (7 x) d x

integral of x[cosh^2(2x^2)-sinh^2(2x^2)]

\int x [cosh^{2} (2 x^{2}) - sinh^{2} (2 x^{2})] d x

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

\int \frac{x + 5}{( x + 2 ) ( x ^{2} - 2 x + 2 ) ^{2}} d x

integral of x^5sqrt(4x^2-1)

\int x^{5} 4 x^{2} - 1 d x

integral of 6xsqrt(x^2-1)

\int 6 x x^{2} - 1 d x