integral from 0 to 1 of (e^x)^3

Lösung

\int_{0}^{1} (e^{x})^{3} d x

\frac{e ^{3} - 1}{3}

Dezimale

6.36184 \dots

Schritte zur Lösung

\int_{0}^{1} (e^{x})^{3} d x

Wende Exponentenregel an:

(a^{b})^{c} = a^{b c}

= \int_{0}^{1} e^{3 x} d x

Wende U-Substitution an

= \int_{0}^{3} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{3} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [e^{u}]_{0}^{3}

Berechne die Grenzen:

e^{3} - 1

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

Vereinfache

= \frac{e ^{3} - 1}{3}

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

\int_{4}^{7} \frac{1}{4 x ^{2} - 8 x - 5} d x

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

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\int_{3}^{12} x^{3} + 3 x + 7 d x