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

Lösung

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

\frac{65}{4} - ln (3) + ln (2)

Dezimale

15.84453 \dots

Schritte zur Lösung

\int_{2}^{3} x^{3} - \frac{1}{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_{2}^{3} x^{3} d x - \int_{2}^{3} \frac{1}{x} d x

\int_{2}^{3} x^{3} d x = \frac{65}{4}

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

= \frac{65}{4} - (ln (3) - ln (2))

Vereinfache

= \frac{65}{4} - ln (3) + ln (2)

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