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Beliebt Rechnen >

integral of (x^2)/(sqrt(x+1))

Lösung

\int \frac{x ^{2}}{x + 1} d x

Lösung

\frac{2}{5} (x + 1)^{\frac{5}{2}} - \frac{4}{3} (x + 1)^{\frac{3}{2}} + 2 x + 1 + C

Schritte zur Lösung

\int \frac{x ^{2}}{x + 1} d x

Wende U-Substitution an

= \int \frac{( u - 1 ) ^{2}}{u} d u

Multipliziere aus

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

= \int u^{\frac{3}{2}} - 2 u + \frac{1}{u} 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^{\frac{3}{2}} d u - \int 2 u d u + \int \frac{1}{u} d u

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

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

\int \frac{1}{u} d u = 2 u

= \frac{2}{5} u^{\frac{5}{2}} - \frac{4}{3} u^{\frac{3}{2}} + 2 u

Setze in

u = x + 1

ein

= \frac{2}{5} (x + 1)^{\frac{5}{2}} - \frac{4}{3} (x + 1)^{\frac{3}{2}} + 2 x + 1

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} (x + 1)^{\frac{5}{2}} - \frac{4}{3} (x + 1)^{\frac{3}{2}} + 2 x + 1 + C

Graph

Beliebte Beispiele

limit as x approaches 0-of 1+e^{1/x}

x \to 0 - lim (1 + e^{\frac{1}{x}})

laplacetransform 3t^2+15t+15

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steigung y=(5x^2-1)^{-3}

s l o p e y = (5 x^{2} - 1)^{- 3}

integral from-infinity to 0 of xe^{8x}

\int_{- \infty}^{0} x e^{8 x} d x

derivative 2x^2-4x

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