integral of 54.0595e^{sqrt(x)}x

Lösung

\int 54.0595 e^{x} x d x

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

Schritte zur Lösung

\int 54.0595 e^{x} x d x

Entferne die Konstante:

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

= 54.0595 \cdot \int e^{x} x d x

Wende U-Substitution an

= 54.0595 \cdot \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

= 54.0595 \cdot 2 \cdot \int e^{u} u^{3} d u

Wende die partielle Integration an

= 54.0595 \cdot 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}))

= 54.0595 \cdot 2 (u^{3} e^{u} - 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u})))

Setze in

u = x

ein

= 54.0595 \cdot 2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x})))

Vereinfache

54.0595 \cdot 2 ((x)^{3} e^{x} - 3 ((x)^{2} e^{x} - 2 (e^{x} x - e^{x}))) : 108.119 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

= 108.119 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x})))

Füge eine Konstante zur Lösung hinzu

= 108.119 (e^{x} x^{\frac{3}{2}} - 3 (e^{x} x - 2 (e^{x} x - e^{x}))) + C

\frac{\partial}{\partial x} (in \frac{x + y}{x - y})

\frac{d}{d x} (\frac{x ^{2}}{( x + 2 i ) ^{2}})

v^{'} = \frac{8 \cdot 9.8 + 3.1 v ^{2}}{8}

x \to 3 lim (\frac{x ^{2} + 1}{10})

y^{^{''}} - 5 y^{^{'}} = 8 t