integral from 0 to 1 of e^xsqrt(e^x+1)

Lösung

\int_{0}^{1} e^{x} e^{x} + 1 d x

\frac{2 ( e + 1 ) ^{\frac{3}{2}} - 4 2}{3}

Dezimale

2.89431 \dots

Schritte zur Lösung

\int_{0}^{1} e^{x} e^{x} + 1 d x

Wende U-Substitution an

= \int_{2}^{e + 1} u d u

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{2 ( e + 1 ) ^{\frac{3}{2}} - 4 2}{3}

= \frac{2 ( e + 1 ) ^{\frac{3}{2}} - 4 2}{3}

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