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Beliebt Rechnen >

integral from 0 to 1 of (x^2+1)e^{2x}

Lösung

\int_{0}^{1} (x^{2} + 1) e^{2 x} d x

Lösung

\frac{3 e ^{2} - 3}{4}

+1

Dezimale

4.79179 \dots

Schritte zur Lösung

\int_{0}^{1} (x^{2} + 1) e^{2 x} d x

Wende die partielle Integration an

= [\frac{1}{2} e^{2 x} (x^{2} + 1) - \int e^{2 x} x d x]_{0}^{1}

\int e^{2 x} x d x = \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})

= [\frac{1}{2} e^{2 x} (x^{2} + 1) - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})]_{0}^{1}

Vereinfache

[\frac{1}{2} e^{2 x} (x^{2} + 1) - \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x})]_{0}^{1} : [\frac{1}{4} (2 e^{2 x} x^{2} - 2 e^{2 x} x + 3 e^{2 x})]_{0}^{1}

= [\frac{1}{4} (2 e^{2 x} x^{2} - 2 e^{2 x} x + 3 e^{2 x})]_{0}^{1}

Berechne die Grenzen:

\frac{3 e ^{2}}{4} - \frac{3}{4}

= \frac{3 e ^{2}}{4} - \frac{3}{4}

Vereinfache

= \frac{3 e ^{2} - 3}{4}

Graph

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