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Beliebt Rechnen >

integral from 0 to 4 of xe^{2x}

Lösung

\int_{0}^{4} x e^{2 x} d x

Lösung

\frac{7 e ^{8} + 1}{4}

+1

Dezimale

5216.92647 \dots

Schritte zur Lösung

\int_{0}^{4} x e^{2 x} d x

Wende U-Substitution an

= \int_{0}^{8} \frac{e ^{u} u}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{0}^{8} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{4} [e^{u} u - \int e^{u} d u]_{0}^{8}

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

= \frac{1}{4} [e^{u} u - e^{u}]_{0}^{8}

Berechne die Grenzen:

7 e^{8} + 1

= \frac{1}{4} (7 e^{8} + 1)

Vereinfache

= \frac{7 e ^{8} + 1}{4}

Graph

Beliebte Beispiele

integral from 1 to e^x of 4ln(x)

\int_{1}^{e^{x}} 4 ln (x) d x

integral from 0 to 1 of 2xy

\int_{0}^{1} 2 x y d x

integral from 0 to x of 3/x

\int_{0}^{x} \frac{3}{x} d x

integral from 0 to 5 of 1/(sqrt(5-x))

\int_{0}^{5} \frac{1}{5 - x} d x

integral from 0 to 5 of-x^2+9

\int_{0}^{5} - x^{2} + 9 d x