integral of 1/(x^{8/9)(8+x^{1/9})}

Lösung

\int \frac{1}{x ^{\frac{8}{9}} ( 8 + x ^{\frac{1}{9}} )} d x

9 ln 8 + x^{\frac{1}{9}} + C

Schritte zur Lösung

\int \frac{1}{x ^{\frac{8}{9}} ( 8 + x ^{\frac{1}{9}} )} d x

Wende U-Substitution an

= \int \frac{9}{u} d u

Entferne die Konstante:

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

= 9 \cdot \int \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 9 ln ∣ u ∣

Setze in

u = 8 + x^{\frac{1}{9}}

ein

= 9 ln 8 + x^{\frac{1}{9}}

Füge eine Konstante zur Lösung hinzu

= 9 ln 8 + x^{\frac{1}{9}} + C

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