integral from 1 to 3 of 2(1+ln(x))x^{2x}

Lösung

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

728

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{3} (1 + ln (x)) x^{2 x} d x

Wende U-Substitution an

= 2 \cdot \int_{1}^{729} \frac{1}{2} d u

Integral einer Konstanten :

\int a d x = a x

= 2 [\frac{1}{2} u]_{1}^{729}

Berechne die Grenzen:

364

= 2 \cdot 364

Vereinfache

= 728

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