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

Lösung

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

\frac{ln ^{2} ( 5 ) ln ( 3 )}{2}

Dezimale

1.42286 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{ln ^{2} ( 5 )}{2} [ln ∣ x ∣]_{1}^{3}

Berechne die Grenzen:

ln (3)

= \frac{ln ^{2} ( 5 )}{2} ln (3)

Vereinfache

= \frac{ln ^{2} ( 5 ) ln ( 3 )}{2}

\int_{0}^{1} 5 x 5^{x} d x

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

\int_{0}^{x} t (t - sin (t)) d t

\int_{0}^{4} x (x^{2} - 1) d x

\int_{0}^{4} \frac{1}{6 x + 1} d x