integral of (ln(x))^4

Lösung

\int (ln (x))^{4} d x

x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))) + C

Schritte zur Lösung

\int (ln (x))^{4} d x

Vereinfache

= \int ln^{4} (x) d x

Wende die partielle Integration an

= x ln^{4} (x) - \int 4 ln^{3} (x) d x

\int 4 ln^{3} (x) d x = 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)))

= x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)))

Füge eine Konstante zur Lösung hinzu

= x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))) + C

n = 0 \sum \infty \frac{n x ^{n}}{n + 1}

\frac{\partial}{\partial y} (y e^{x^{2} - y})

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

\frac{d}{d x} ((2 x^{2} - 7 x + 6)^{2})

l a pl a ce t r an s f or m 7