integral from x^3 to x of e^{(2y)/x}

Lösung

\int_{x^{3}}^{x} e^{\frac{2 y}{x}} d y

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

Schritte zur Lösung

\int_{x^{3}}^{x} e^{\frac{2 y}{x}} d y

Wende U-Substitution an

= \int_{2 x^{2}}^{2} \frac{x e ^{u}}{2} d u

Entferne die Konstante:

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

= \frac{x}{2} \cdot \int_{2 x^{2}}^{2} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{x}{2} [e^{u}]_{2 x^{2}}^{2}

Berechne die Grenzen:

e^{2} - e^{2 x^{2}}

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

Vereinfache

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

\int_{- \infty}^{0} \frac{x}{e ^{x}} d x

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\int_{0}^{4} (4 - x^{2}) d x

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