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Beliebt Rechnen >

integral from 1 to 2 of xe^{x^2}

Lösung

\int_{1}^{2} x e^{x^{2}} d x

Lösung

\frac{e ^{4} - e}{2}

+1

Dezimale

25.93993 \dots

Schritte zur Lösung

\int_{1}^{2} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{1}^{4} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{4} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{1}^{4}

Berechne die Grenzen:

e^{4} - e

= \frac{1}{2} (e^{4} - e)

Vereinfache

= \frac{e ^{4} - e}{2}

Graph

Beliebte Beispiele

\frac{d y}{d x} = (4 y)

derivative of (3x^2+4(2x-3))

\frac{d}{d x} ((3 x^{2} + 4) (2 x - 3))

integral of 5/x+e^x

\int \frac{5}{x} + e^{x} d x

tangent y=5+5x^2-2x^3

t an g e n t y = 5 + 5 x^{2} - 2 x^{3}

integral of (x-5)^2e^x

\int (x - 5)^{2} e^{x} d x