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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{3 e ^{4} + 1}{4}

+1

Dezimale

41.19861 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

3 e^{4} + 1

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

Vereinfache

= \frac{3 e ^{4} + 1}{4}

Graph

Beliebte Beispiele

integral from 1 to infinity of sin^2(x)

\int_{1}^{\infty} sin^{2} (x) d x

derivative of cot(x^4)

\frac{d}{d x} (cot (x^{4}))

derivative of (x^2/2-(x^7)/7)

\frac{d}{d x} (\frac{x ^{2}}{2} - \frac{x ^{7}}{7})

(2xy^2+y)dx+(2x^2y+x)dy=0

(2 x y^{2} + y) d x + (2 x^{2} y + x) d y = 0

integral of (7t-5)/(t+1)

\int \frac{7 t - 5}{t + 1} d t