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Beliebt Rechnen >

integral from 1 to 5 of (3(ln(x))^2)/x

Lösung

\int_{1}^{5} \frac{3 ( ln ( x ) ) ^{2}}{x} d x

Lösung

ln^{3} (5)

+1

Dezimale

4.16891 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{3 ( ln ( x ) ) ^{2}}{x} d x

Entferne die Konstante:

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

= 3 \cdot \int_{1}^{5} \frac{( ln ( x ) ) ^{2}}{x} d x

Wende U-Substitution an

= 3 \cdot \int_{0}^{l n (5)} u^{2} d u

Wende die Potenzregel an

= 3 [\frac{u ^{3}}{3}]_{0}^{l n (5)}

Berechne die Grenzen:

\frac{ln ^{3} ( 5 )}{3}

= 3 \cdot \frac{ln ^{3} ( 5 )}{3}

Vereinfache

= ln^{3} (5)

Graph

Beliebte Beispiele

integral from 0 to 2 of (x(1+3y^2))/4

\int_{0}^{2} \frac{x ( 1 + 3 y ^{2} )}{4} d x

integral from 1 to 2 of x^2y

\int_{1}^{2} x^{2} y d y

integral from 2 to 5 of 2

\int_{2}^{5} 2 d x

integral from 0 to pi/4 of cos(x^2)

\int_{0}^{\frac{π}{4}} cos (x^{2}) d x

integral from-1 to 5 of 1+3x

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