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Beliebt Rechnen >

integral of x^5sqrt(x^3)+4

Lösung

\int x^{5} x^{3} + 4 d x

Lösung

\frac{2}{15} x^{\frac{15}{2}} + 4 x + C

Schritte zur Lösung

\int x^{5} x^{3} + 4 d x

x^{3} = x^{\frac{3}{2}},

angenommen

x \geq 0

= \int x^{5} x^{\frac{3}{2}} + 4 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{5} x^{\frac{3}{2}} d x + \int 4 d x

\int x^{5} x^{\frac{3}{2}} d x = \frac{2}{15} x^{\frac{15}{2}}

\int 4 d x = 4 x

= \frac{2}{15} x^{\frac{15}{2}} + 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{15} x^{\frac{15}{2}} + 4 x + C

Graph

Beliebte Beispiele

integral from 0 to pi/(21) of tan(7x)

\int_{0}^{\frac{π}{21}} tan (7 x) d x

y^{^{'}} + 2 y = 1

integral of (x+4)e^{x^2+8x}

\int (x + 4) e^{x^{2} + 8 x} d x

derivative y=x^2cos(x)

d er i v a t i v e y = x^{2} cos (x)

(dy)/(dx)=4xsqrt(4-y^2)

\frac{d y}{d x} = 4 x 4 - y^{2}