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Beliebt Rechnen >

integral of xe^{sqrt(x)}

Lösung

\int x e^{x} d x

Lösung

2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x}))) + C

Schritte zur Lösung

\int x e^{x} d x

Wende U-Substitution an

= \int 2 e^{u} u^{3} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int e^{u} u^{3} d u

Wende die partielle Integration an

= 2 (u^{3} e^{u} - \int 3 u^{2} e^{u} d u)

\int 3 u^{2} e^{u} d u = 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u}))

= 2 (u^{3} e^{u} - 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u})))

Setze in

u = x

ein

= 2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x})))

Vereinfache

2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x}))) : 2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

= 2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

Füge eine Konstante zur Lösung hinzu

= 2 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x}))) + C

Graph

Beliebte Beispiele

integral from 0 to 1 of (e^z+1)/(e^z+z)

\int_{0}^{1} \frac{e ^{z} + 1}{e ^{z} + z} d z

(dy)/(dx)=40-3y

\frac{d y}{d x} = 40 - 3 y

integral of x^3cos(x^4+1)

\int x^{3} cos (x^{4} + 1) d x

integral of (6+x^9)^5x^8

\int (6 + x^{9})^{5} x^{8} d x

limit as h approaches infinity of (3h+2xh^2+x^2+h^3)/(4-3xh-2x^3h^3)

h \to \infty lim (\frac{3 h + 2 x h ^{2} + x ^{2} + h ^{3}}{4 - 3 x h - 2 x ^{3} h ^{3}})