integral from 1 to e of (2+3ln(x))/x

Lösung

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

\frac{7}{2}

Dezimale

3.5

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{5} \frac{u}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{2}^{5} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{2}}{2}]_{2}^{5}

Berechne die Grenzen:

\frac{21}{2}

= \frac{1}{3} \cdot \frac{21}{2}

Vereinfache

= \frac{7}{2}

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