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)/(sqrt(x^2+9))

Lösung

\int \frac{x ^{3}}{x ^{2} + 9} d x

Lösung

\frac{1}{3} (x^{2} + 9)^{\frac{3}{2}} - 9 x^{2} + 9 + C

Schritte zur Lösung

\int \frac{x ^{3}}{x ^{2} + 9} d x

Wende U-Substitution an

= \int u^{2} - 9 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

= \int u^{2} d u - \int 9 d u

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

\int 9 d u = 9 u

= \frac{u ^{3}}{3} - 9 u

Setze in

u = x^{2} + 9

ein

= \frac{( x ^{2} + 9 ) ^{3}}{3} - 9 x^{2} + 9

Vereinfache

\frac{( x ^{2} + 9 ) ^{3}}{3} - 9 x^{2} + 9 : \frac{1}{3} (x^{2} + 9)^{\frac{3}{2}} - 9 x^{2} + 9

= \frac{1}{3} (x^{2} + 9)^{\frac{3}{2}} - 9 x^{2} + 9

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (x^{2} + 9)^{\frac{3}{2}} - 9 x^{2} + 9 + C

Graph

Beliebte Beispiele

derivative of (-2x^2-2/((x-1)^2(x+1)^2))

\frac{d}{d x} (\frac{- 2 x ^{2} - 2}{( x - 1 ) ^{2} ( x + 1 ) ^{2}})

fläche x=(y-1)^2,x=13-y^2

a re a x = (y - 1)^{2}, x = 13 - y^{2}

integral of (2x)/(e^{2x)}

\int \frac{2 x}{e ^{2 x}} d x

limit as x approaches 2+of g(x)

x \to 2 + lim (g (x))

derivative of arctan(8^x)

\frac{d}{d x} (arctan (8^{x}))