integral from 0 to 1 of 16x^3ln(x)

Lösung

\int_{0}^{1} 16 x^{3} ln (x) d x

- 1

Schritte zur Lösung

\int_{0}^{1} 16 x^{3} ln (x) d x

Entferne die Konstante:

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

= 16 \cdot \int_{0}^{1} x^{3} ln (x) d x

Wende die partielle Integration an

= 16 [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{0}^{1}

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

= 16 [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{0}^{1}

Berechne die Grenzen:

- \frac{1}{16}

= 16 (- \frac{1}{16})

Vereinfache

= - 1

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\int_{0}^{2} \frac{x ^{2}}{x ^{3} + 1} d x