integral from 1 to 2 of x^4ln(3x)

Lösung

\int_{1}^{2} x^{4} ln (3 x) d x

- \frac{31}{25} + \frac{ln ( 2 ^{32} \cdot 3 ^{31} )}{5}

Dezimale

10.00753 \dots

Schritte zur Lösung

\int_{1}^{2} x^{4} ln (3 x) d x

Wende die partielle Integration an

= [\frac{1}{5} x^{5} ln (3 x) - \int \frac{x ^{4}}{5} d x]_{1}^{2}

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= [\frac{1}{5} x^{5} ln (3 x) - \frac{x ^{5}}{25}]_{1}^{2}

Berechne die Grenzen:

- \frac{31}{25} + \frac{32 ln ( 6 ) - ln ( 3 )}{5}

= - \frac{31}{25} + \frac{32 ln ( 6 ) - ln ( 3 )}{5}

Vereinfache

= - \frac{31}{25} + \frac{ln ( 2 ^{32} \cdot 3 ^{31} )}{5}

\int_{0}^{3} (3 - x^{2}) d x

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