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

Lösung

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

2

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= \frac{1}{4} \cdot \int_{0}^{4} v d v

Wende die Potenzregel an

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

Berechne die Grenzen:

8

= \frac{1}{4} \cdot 8

Vereinfache

= 2

\int_{1}^{l n (8)} e^{y} (y - 1) d y

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\int_{- 1}^{1} x^{299} d x