integral of xln^2(x)

Lösung

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

\frac{1}{2} x^{2} ln^{2} (x) - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int x ln (x) d x = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}

= \frac{1}{2} x^{2} ln^{2} (x) - (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4})

Vereinfache

= \frac{1}{2} x^{2} ln^{2} (x) - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} ln^{2} (x) - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4} + C

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{23}{2}}} d x

x \to 10 - lim (ln (100 - x^{2}))

x \to \infty + lim (i x)

\int_{0}^{\frac{π}{2}} 1

\frac{d}{d x} (\frac{2}{x + 8})