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Beliebt Rechnen >

integral from 1 to 2 of (ln(x^7))/x

Lösung

\int_{1}^{2} \frac{ln ( x ^{7} )}{x} d x

Lösung

\frac{7 ln ^{2} ( 2 )}{2}

+1

Dezimale

1.68158 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{ln ( x ^{7} )}{x} d x

Wende U-Substitution an

= \int_{1}^{128} \frac{ln ( u )}{7 u} d u

Entferne die Konstante:

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

= \frac{1}{7} \cdot \int_{1}^{128} \frac{ln ( u )}{u} d u

Wende U-Substitution an

= \frac{1}{7} \cdot \int_{0}^{7 l n (2)} v d v

Wende die Potenzregel an

= \frac{1}{7} [\frac{v ^{2}}{2}]_{0}^{7 l n (2)}

Berechne die Grenzen:

\frac{49 ln ^{2} ( 2 )}{2}

= \frac{1}{7} \cdot \frac{49 ln ^{2} ( 2 )}{2}

Vereinfache

= \frac{7 ln ^{2} ( 2 )}{2}

Graph

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\int_{- 2}^{2} 2 + ∣ x ∣ d x

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