integral from 1 to e of (4ln(x))/x

Lösung

\int_{1}^{e} \frac{4 ln ( x )}{x} d x

2

Schritte zur Lösung

\int_{1}^{e} \frac{4 ln ( x )}{x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{e} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{1} u d u

Wende die Potenzregel an

= 4 [\frac{u ^{2}}{2}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= 4 \cdot \frac{1}{2}

Vereinfache

= 2

\int_{0}^{\infty} t d t

\int_{0}^{1} (5 x^{3} - \frac{1}{2}) d x

\int_{1}^{6} t^{2} - 4 t - 12 d t

\int_{- 7}^{8} \frac{1}{2} x d x

\int_{0}^{6} - \frac{5}{12} x^{2} - 5 x d x