integral from 1 to e of (10ln(x))/x

Lösung

\int_{1}^{e} \frac{10 ln ( x )}{x} d x

5

Schritte zur Lösung

\int_{1}^{e} \frac{10 ln ( x )}{x} d x

Entferne die Konstante:

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

= 10 \cdot \int_{1}^{e} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 10 \cdot \int_{0}^{1} u d u

Wende die Potenzregel an

= 10 [\frac{u ^{2}}{2}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= 10 \cdot \frac{1}{2}

Vereinfache

= 5

\int_{0}^{x} \frac{5}{1 + 5 x ^{2}} d x

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

\int_{a}^{10 b} 2 s d s

\int_{- 1}^{1} 3 x^{5} - 3 x^{2} - 3 x + 3 d x

\int_{0}^{2} (3 x^{2} e^{2 x^{3}}) d x