integral from 1 to 2 of 4xe^{2x}

Lösung

\int_{1}^{2} 4 x e^{2 x} d x

3 e^{4} - e^{2}

Dezimale

156.40539 \dots

Schritte zur Lösung

\int_{1}^{2} 4 x e^{2 x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{2} x e^{2 x} d x

Wende U-Substitution an

= 4 \cdot \int_{2}^{4} \frac{e ^{u} u}{4} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{4} \cdot \int_{2}^{4} e^{u} u d u

Wende die partielle Integration an

= 4 \cdot \frac{1}{4} [e^{u} u - \int e^{u} d u]_{2}^{4}

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

= 4 \cdot \frac{1}{4} [e^{u} u - e^{u}]_{2}^{4}

Vereinfache

4 \cdot \frac{1}{4} [e^{u} u - e^{u}]_{2}^{4} : [e^{u} u - e^{u}]_{2}^{4}

= [e^{u} u - e^{u}]_{2}^{4}

Berechne die Grenzen:

3 e^{4} - e^{2}

= 3 e^{4} - e^{2}

\int_{- 4}^{2} 2 x + 5 d x

\int_{0}^{x^{3}} ln (t^{2} + 1) d t

\int_{- 4}^{4} \frac{1}{x ^{2}} d x

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

\int_{1}^{a} \frac{1}{x} d x