integral of ln^2(x^{20})

Lösung

\int ln^{2} (x^{20}) d x

400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x) + C

Schritte zur Lösung

\int ln^{2} (x^{20}) d x

Wende die partielle Integration an

= x ln^{2} (x^{20}) - \int 40 ln (x^{20}) d x

\int 40 ln (x^{20}) d x = 40 (20 x ln (x) - 20 x)

= x ln^{2} (x^{20}) - 40 (20 x ln (x) - 20 x)

Vereinfache

x ln^{2} (x^{20}) - 40 (20 x ln (x) - 20 x) : 400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x)

= 400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x)

Füge eine Konstante zur Lösung hinzu

= 400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x) + C

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