integral from 1 to 3 of (x+1)e^{x^2+2x}

Lösung

\int_{1}^{3} (x + 1) e^{x^{2} + 2 x} d x

\frac{e ^{15} - e ^{3}}{2}

Dezimale

1634498.64346 \dots

Schritte zur Lösung

\int_{1}^{3} (x + 1) e^{x^{2} + 2 x} d x

Wende U-Substitution an

= \int_{3}^{15} \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_{3}^{15} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{3}^{15}

Berechne die Grenzen:

e^{15} - e^{3}

= \frac{1}{2} (e^{15} - e^{3})

Vereinfache

= \frac{e ^{15} - e ^{3}}{2}

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