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Beliebt Rechnen >

integral from 0 to 1 of e^{5x}

Lösung

\int_{0}^{1} e^{5 x} d x

Lösung

\frac{e ^{5} - 1}{5}

+1

Dezimale

29.48263 \dots

Schritte zur Lösung

\int_{0}^{1} e^{5 x} d x

Wende U-Substitution an

= \int_{0}^{5} e^{u} \frac{1}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{0}^{5} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{5} [e^{u}]_{0}^{5}

Berechne die Grenzen:

e^{5} - 1

= \frac{1}{5} (e^{5} - 1)

Vereinfache

= \frac{e ^{5} - 1}{5}

Graph

Beliebte Beispiele

limit as y approaches 2 of (y^2-4)/(y+2)

y \to 2 lim (\frac{y ^{2} - 4}{y + 2})

derivative (2x^2+1)^{3/2}

d er i v a t i v e (2 x^{2} + 1)^{\frac{3}{2}}

implicit (dy)/(dx),x^2=(5x+4y)/(5x-4y)

im pl i c i t \frac{d y}{d x}, x^{2} = \frac{5 x + 4 y}{5 x - 4 y}

inverselaplace 2/(3s+1)

in v erse l a pl a ce \frac{2}{3 s + 1}

normal y= 4/(2x+8),(0, 1/2)

n or ma l y = \frac{4}{2 x + 8}, (0, \frac{1}{2})