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

Lösung

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

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

Dezimale

2.90903 \dots

Schritte zur Lösung

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

Multipliziere aus

\frac{1 + ln ( x ^{3} )}{x} : \frac{1}{x} + \frac{ln ( x ^{3} )}{x}

= \int_{1}^{3} \frac{1}{x} + \frac{ln ( x ^{3} )}{x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} \frac{1}{x} d x + \int_{1}^{3} \frac{ln ( x ^{3} )}{x} d x

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

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

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

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