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Beliebt Rechnen >

integral of x^2sqrt(9+x)

Lösung

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

Lösung

\frac{2}{7} (9 + x)^{\frac{7}{2}} - \frac{36}{5} (9 + x)^{\frac{5}{2}} + 54 (9 + x)^{\frac{3}{2}} + C

Schritte zur Lösung

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

Wende U-Substitution an

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

Multipliziere aus

(u - 9)^{2} u : u^{\frac{5}{2}} - 18 u^{\frac{3}{2}} + 81 u

= \int u^{\frac{5}{2}} - 18 u^{\frac{3}{2}} + 81 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{5}{2}} d u - \int 18 u^{\frac{3}{2}} d u + \int 81 u d u

\int u^{\frac{5}{2}} d u = \frac{2}{7} u^{\frac{7}{2}}

\int 18 u^{\frac{3}{2}} d u = \frac{36}{5} u^{\frac{5}{2}}

\int 81 u d u = 54 u^{\frac{3}{2}}

= \frac{2}{7} u^{\frac{7}{2}} - \frac{36}{5} u^{\frac{5}{2}} + 54 u^{\frac{3}{2}}

Setze in

u = 9 + x

ein

= \frac{2}{7} (9 + x)^{\frac{7}{2}} - \frac{36}{5} (9 + x)^{\frac{5}{2}} + 54 (9 + x)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} (9 + x)^{\frac{7}{2}} - \frac{36}{5} (9 + x)^{\frac{5}{2}} + 54 (9 + x)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

steigung x/(x^2+1)

s l o p e \frac{x}{x ^{2} + 1}

(x^2+1)(dy)/(dx)+6x(y-1)=0,y(0)=8

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0, y (0) = 8

integral of (x+6)^4

\int (x + 6)^{4} d x

fläche y=x,y=sqrt(x),x=0,x=2

a re a y = x, y = x, x = 0, x = 2

derivative f(x)=xsqrt(x^2+1)

d er i v a t i v e f (x) = x x^{2} + 1