integral from 0 to 1 of xe^{x^2}

Lösung

\int_{0}^{1} x e^{x^{2}} d x

\frac{e - 1}{2}

Dezimale

0.85914 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{0}^{1} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{0}^{1}

Berechne die Grenzen:

e - 1

= \frac{1}{2} (e - 1)

Vereinfache

= \frac{e - 1}{2}

\int \frac{ln ^{5} ( x )}{x} d x

y^{^{'}} = \frac{( 2 y + 3 ) ^{2}}{( 4 x + 5 ) ^{2}}

\frac{\partial}{\partial y} ((x + 2 y)^{2})

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

\int \frac{( 5 x ^{2} )}{1 - 5 x ^{3}} d x