integral from 1 to e^3 of (6ln(x))/x

Lösung

\int_{1}^{e^{3}} \frac{6 ln ( x )}{x} d x

27

Schritte zur Lösung

\int_{1}^{e^{3}} \frac{6 ln ( x )}{x} d x

Entferne die Konstante:

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

= 6 \cdot \int_{1}^{e^{3}} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 6 \cdot \int_{0}^{3} u d u

Wende die Potenzregel an

= 6 [\frac{u ^{2}}{2}]_{0}^{3}

Berechne die Grenzen:

\frac{9}{2}

= 6 \cdot \frac{9}{2}

Vereinfache

= 27

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

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

\int_{\frac{1}{3}}^{5} 1 + 36 x d x

\int_{2}^{3} x x^{2} - 4 d x

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