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Beliebt Rechnen >

integral from 0 to 1 of (e^x+1)/(e^x+x)

Lösung

\int_{0}^{1} \frac{e ^{x} + 1}{e ^{x} + x} d x

Lösung

ln (e + 1)

+1

Dezimale

1.31326 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{e ^{x} + 1}{e ^{x} + x} d x

Wende U-Substitution an

= \int_{1}^{e + 1} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{e + 1}

Berechne die Grenzen:

ln (e + 1)

= ln (e + 1)

Graph

Beliebte Beispiele

y^'=ysin(x),y(0)=1

y^{^{'}} = y sin (x), y (0) = 1

1/6 y^{''}+6y=tan(6t)-1/2 e^{3t}

\frac{1}{6} y^{^{''}} + 6 y = tan (6 t) - \frac{1}{2} e^{3 t}

(\partial)/(\partial x)(tan(y))

\frac{\partial}{\partial x} (tan (y))

(dy)/(dx)=((2880-y))/(320)

\frac{d y}{d x} = \frac{( 2880 - y )}{320}

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