integral from 2 to 4 of x^2e^{x^3+5}

Lösung

\int_{2}^{4} x^{2} e^{x^{3} + 5} d x

\frac{e ^{69} - e ^{13}}{3}

Dezimale

3.08459 E 29

Schritte zur Lösung

\int_{2}^{4} x^{2} e^{x^{3} + 5} d x

Wende U-Substitution an

= \int_{13}^{69} \frac{e ^{u}}{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_{13}^{69} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [e^{u}]_{13}^{69}

Berechne die Grenzen:

e^{69} - e^{13}

= \frac{1}{3} (e^{69} - e^{13})

Vereinfache

= \frac{e ^{69} - e ^{13}}{3}

\int_{- 1}^{5} (4 x^{3} - 3 x^{2} + 1) x d x

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