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Beliebt Rechnen >

integral from 0 to 1 of xe^{9x}

Lösung

\int_{0}^{1} x e^{9 x} d x

Lösung

\frac{8 e ^{9} + 1}{81}

+1

Dezimale

800.31693 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{9 x} d x

Wende U-Substitution an

= \int_{0}^{9} \frac{e ^{u} u}{81} d u

Entferne die Konstante:

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

= \frac{1}{81} \cdot \int_{0}^{9} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{81} [e^{u} u - \int e^{u} d u]_{0}^{9}

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

= \frac{1}{81} [e^{u} u - e^{u}]_{0}^{9}

Berechne die Grenzen:

8 e^{9} + 1

= \frac{1}{81} (8 e^{9} + 1)

Vereinfache

= \frac{8 e ^{9} + 1}{81}

Graph

Beliebte Beispiele

(\partial)/(\partial y)(e^{-9t}cos(pix))

\frac{\partial}{\partial y} (e^{- 9 t} cos (π x))

derivative of (1-sin(x)^3)

\frac{d}{d x} ((1 - sin (x))^{3})

integral of x/(e^{-x)}

\int \frac{x}{e ^{- x}} d x

derivative of 2x^2-3x+1

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

taylor-(x-3)^3,1

t a y l or - (x - 3)^{3}, 1