integral from 0 to 5 of xe^{2x}

Lösung

\int_{0}^{5} x e^{2 x} d x

\frac{9 e ^{10} + 1}{4}

Dezimale

49559.79803 \dots

Schritte zur Lösung

\int_{0}^{5} x e^{2 x} d x

Wende U-Substitution an

= \int_{0}^{10} \frac{e ^{u} u}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{0}^{10} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{4} [e^{u} u - \int e^{u} d u]_{0}^{10}

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

= \frac{1}{4} [e^{u} u - e^{u}]_{0}^{10}

Berechne die Grenzen:

9 e^{10} + 1

= \frac{1}{4} (9 e^{10} + 1)

Vereinfache

= \frac{9 e ^{10} + 1}{4}

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