integral of xe^{2/5 x^2+7}

Lösung

\int x e^{\frac{2}{5} x^{2} + 7} d x

\frac{5}{4} e^{\frac{2}{5} x^{2} + 7} + C

Schritte zur Lösung

\int x e^{\frac{2}{5} x^{2} + 7} d x

Wende U-Substitution an

= \int \frac{5 e ^{u}}{4} d u

Entferne die Konstante:

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

= \frac{5}{4} \cdot \int e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{5}{4} e^{u}

Setze in

u = \frac{2}{5} x^{2} + 7

ein

= \frac{5}{4} e^{\frac{2}{5} x^{2} + 7}

Füge eine Konstante zur Lösung hinzu

= \frac{5}{4} e^{\frac{2}{5} x^{2} + 7} + C

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