integral from 1 to 4 of 7/(xln(7x))

Lösung

\int_{1}^{4} \frac{7}{x ln ( 7 x )} d x

7 (ln (ln (28)) - ln (ln (7)))

Dezimale

3.76533 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{7}{x ln ( 7 x )} d x

Entferne die Konstante:

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

= 7 \cdot \int_{1}^{4} \frac{1}{x ln ( 7 x )} d x

Wende U-Substitution an

= 7 \cdot \int_{7}^{28} \frac{1}{u ln ( u )} d u

Wende U-Substitution an

= 7 \cdot \int_{l n (7)}^{l n (28)} \frac{1}{v} d v

Nutze das gemeinsame Integral :

\int \frac{1}{v} d v = ln (∣ v ∣)

= 7 [ln ∣ v ∣]_{l n (7)}^{l n (28)}

Berechne die Grenzen:

ln (ln (28)) - ln (ln (7))

= 7 (ln (ln (28)) - ln (ln (7)))