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

taylor sin(2x),0

t a y l or sin (2 x), 0

d/(dt)((e^{-t})/(1+t^2))

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

derivative arcsec(x)*arccos(x)

d er i v a t i v e arcsec (x) \cdot arccos (x)

integral of te^{t+2}

\int t e^{t + 2} d t

integral of ()/(m^3+m^2)

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