integral from 1 to e^5 of (10ln(x))/x

Lösung

\int_{1}^{e^{5}} \frac{10 ln ( x )}{x} d x

125

Schritte zur Lösung

\int_{1}^{e^{5}} \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^{5}} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 10 \cdot \int_{0}^{5} u d u

Wende die Potenzregel an

= 10 [\frac{u ^{2}}{2}]_{0}^{5}

Berechne die Grenzen:

\frac{25}{2}

= 10 \cdot \frac{25}{2}

Vereinfache

= 125

\int_{0}^{3} (8 x - 1)^{2} d x

\int_{0}^{1} y 4 y^{2} + 1 d y

\int_{0}^{4} \frac{x}{1 + x} d x

\int_{1}^{8} f (t) d t

\int_{0}^{1} y^{\frac{1}{3}} d y