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Beliebt Rechnen >

integral of x^2*sqrt(x-5)

Lösung

\int x^{2} \cdot x - 5 d x

Lösung

\frac{2}{7} (x - 5)^{\frac{7}{2}} + 4 (x - 5)^{\frac{5}{2}} + \frac{50}{3} (x - 5)^{\frac{3}{2}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int (u + 5)^{2} u d u

Multipliziere aus

(u + 5)^{2} u : u^{\frac{5}{2}} + 10 u^{\frac{3}{2}} + 25 u

= \int u^{\frac{5}{2}} + 10 u^{\frac{3}{2}} + 25 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 10 u^{\frac{3}{2}} d u + \int 25 u d u

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

\int 10 u^{\frac{3}{2}} d u = 4 u^{\frac{5}{2}}

\int 25 u d u = \frac{50}{3} u^{\frac{3}{2}}

= \frac{2}{7} u^{\frac{7}{2}} + 4 u^{\frac{5}{2}} + \frac{50}{3} u^{\frac{3}{2}}

Setze in

u = x - 5

ein

= \frac{2}{7} (x - 5)^{\frac{7}{2}} + 4 (x - 5)^{\frac{5}{2}} + \frac{50}{3} (x - 5)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} (x - 5)^{\frac{7}{2}} + 4 (x - 5)^{\frac{5}{2}} + \frac{50}{3} (x - 5)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

derivative y=x^2(x^3-1)^5

d er i v a t i v e y = x^{2} (x^{3} - 1)^{5}

normal y=sqrt(2x+1),\at x=4

n or ma l y = 2 x + 1, at x = 4

f^'(x)=x^4-3x^3-6x^2+6x-1

f^{^{'}} (x) = x^{4} - 3 x^{3} - 6 x^{2} + 6 x - 1

integral from 0 to 2 of 1/(sqrt(16-x^2))

\int_{0}^{2} \frac{1}{16 - x ^{2}} d x

sum from n=1 to infinity of cos(4n)

n = 1 \sum \infty cos (4 n)