integral from 3 to 7 of t^5ln(t)

Lösung

\int_{3}^{7} t^{5} ln (t) d t

- \frac{29230}{9} + \frac{117649}{6} ln (7) - \frac{243}{2} ln (3)

Dezimale

34774.47135 \dots

Schritte zur Lösung

\int_{3}^{7} t^{5} ln (t) d t

Wende die partielle Integration an

= [\frac{1}{6} t^{6} ln (t) - \int \frac{t ^{5}}{6} d t]_{3}^{7}

\int \frac{t ^{5}}{6} d t = \frac{t ^{6}}{36}

= [\frac{1}{6} t^{6} ln (t) - \frac{t ^{6}}{36}]_{3}^{7}

Berechne die Grenzen:

- \frac{29230}{9} + \frac{117649}{6} ln (7) - \frac{243}{2} ln (3)

= - \frac{29230}{9} + \frac{117649}{6} ln (7) - \frac{243}{2} ln (3)

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