integral from 1 to e^{3x of}(ln(t))^2

Lösung

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

9 x^{2} e^{3 x} - 2 (3 x e^{3 x} - e^{3 x}) - 2

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int 2 ln (t) d t = 2 (t ln (t) - t)

= [t ln^{2} (t) - 2 (t ln (t) - t)]_{1}^{e^{3 x}}

Berechne die Grenzen:

9 x^{2} e^{3 x} - 2 (3 x e^{3 x} - e^{3 x}) - 2

= 9 x^{2} e^{3 x} - 2 (3 x e^{3 x} - e^{3 x}) - 2

\int_{0}^{4} (x^{3} + 5) d x

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