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Beliebt Rechnen >

integral of 1/(xsqrt(1+ln(x^5)))

Lösung

\int \frac{1}{x 1 + ln ( x ^{5} )} d x

Lösung

\frac{2}{5} 1 + 5 ln (x) + C

Schritte zur Lösung

\int \frac{1}{x 1 + ln ( x ^{5} )} d x

1 + ln (x^{5}) = 1 + 5 ln (x)

= \int \frac{1}{x 1 + 5 ln ( x )} d x

Wende U-Substitution an

= \int \frac{1}{5 u} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{5} \cdot 2 u^{\frac{1}{2}}

Setze in

u = 1 + 5 ln (x)

ein

= \frac{1}{5} \cdot 2 (1 + 5 ln (x))^{\frac{1}{2}}

Vereinfache

\frac{1}{5} \cdot 2 (1 + 5 ln (x))^{\frac{1}{2}} : \frac{2}{5} 1 + 5 ln (x)

= \frac{2}{5} 1 + 5 ln (x)

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} 1 + 5 ln (x) + C

Graph

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