integral from 0 to 1 of 5xe^x

Lösung

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

5

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= 5 [e^{x} x - \int e^{x} d x]_{0}^{1}

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

= 5 [e^{x} x - e^{x}]_{0}^{1}

Berechne die Grenzen:

1

= 5 \cdot 1

Vereinfache

= 5

\int_{0}^{1} 3 x^{2} - 1 d x

\int_{0}^{0.3} ln (1 + x^{2}) d x

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

\int_{1}^{2} (2 x^{3} - 2 x^{2} - 4 x - 1) d x

\int_{- π}^{0} 4 x^{4} d x