integral from 1 to 3 of xe^{3x}

Lösung

\int_{1}^{3} x e^{3 x} d x

\frac{8 e ^{9} - 2 e ^{3}}{9}

Dezimale

7198.27781 \dots

Schritte zur Lösung

\int_{1}^{3} x e^{3 x} d x

Wende U-Substitution an

= \int_{3}^{9} \frac{e ^{u} u}{9} d u

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int_{3}^{9} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{9} [e^{u} u - \int e^{u} d u]_{3}^{9}

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

= \frac{1}{9} [e^{u} u - e^{u}]_{3}^{9}

Berechne die Grenzen:

8 e^{9} - 2 e^{3}

= \frac{1}{9} (8 e^{9} - 2 e^{3})

Vereinfache

= \frac{8 e ^{9} - 2 e ^{3}}{9}