integral from 2 to 4 of-4x^3ln(x)

Lösung

\int_{2}^{4} - 4 x^{3} ln (x) d x

- 4 (124 ln (2) - 15)

Dezimale

- 283.80100 \dots

Schritte zur Lösung

\int_{2}^{4} - 4 x^{3} ln (x) d x

Entferne die Konstante:

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

= - 4 \cdot \int_{2}^{4} x^{3} ln (x) d x

Wende die partielle Integration an

= - 4 [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{2}^{4}

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= - 4 [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{2}^{4}

Berechne die Grenzen:

124 ln (2) - 15

= - 4 (124 ln (2) - 15)

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