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

Lösung

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

\frac{4 x ^{12} ln ( x )}{3} + \frac{- x ^{12} + 1}{9}

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{t ^{2}}{3} d t = \frac{t ^{3}}{9}

= [\frac{1}{3} t^{3} ln (t) - \frac{t ^{3}}{9}]_{1}^{x^{4}}

Berechne die Grenzen:

\frac{4}{3} x^{12} ln (x) - \frac{x ^{12}}{9} + \frac{1}{9}

= \frac{4}{3} x^{12} ln (x) - \frac{x ^{12}}{9} + \frac{1}{9}

Vereinfache

= \frac{4 x ^{12} ln ( x )}{3} + \frac{- x ^{12} + 1}{9}

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