de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{7 e ^{8} + 1}{16}

+1

Dezimale

1304.23161 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{8} \frac{e ^{u} u}{16} d u

Entferne die Konstante:

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

= \frac{1}{16} \cdot \int_{0}^{8} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{16} [e^{u} u - \int e^{u} d u]_{0}^{8}

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

= \frac{1}{16} [e^{u} u - e^{u}]_{0}^{8}

Berechne die Grenzen:

7 e^{8} + 1

= \frac{1}{16} (7 e^{8} + 1)

Vereinfache

= \frac{7 e ^{8} + 1}{16}

Graph

Beliebte Beispiele

y^{^{'}} = y^{3}, y (0) = 1

(dy)/(dt)+1/2 y=17sin(2t)

\frac{d y}{d t} + \frac{1}{2} y = 17 sin (2 t)

integral of cos(sqrt(2x))

\int cos (2 x) d x

integral of (tan(x))^4

\int (tan (x))^{4} d x

derivative of (x^2-5x+4/(|x-1|))

\frac{d}{d x} (\frac{x ^{2} - 5 x + 4}{∣ x - 1 ∣})