integral of x^2(ln(x))^2

Lösung

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

\frac{1}{3} x^{3} ln^{2} (x) - \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{3} x^{3} ln^{2} (x) - \int \frac{2}{3} x^{2} ln (x) d x

\int \frac{2}{3} x^{2} ln (x) d x = \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

= \frac{1}{3} x^{3} ln^{2} (x) - \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} ln^{2} (x) - \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

d er i v a t i v e y = - 6 x

\int (\frac{2}{x ^{3}} + x^{4}) d x

\frac{d}{d x} (ln (tan (2 x)))

\frac{\partial}{\partial t} (1 - cos (t))

\frac{d}{d x} (\frac{8}{x ^{7}})