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Beliebt Rechnen >

integral of ln^4(x)

Lösung

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

Lösung

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^{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

Graph

Beliebte Beispiele

d/(dt)(sin(pi)t)

\frac{d}{d t} (sin (π) t)

d/(dy)(A/(y^7)+Be^y)

\frac{d}{d y} (\frac{A}{y ^{7}} + B e^{y})

integral of 6sqrt(x)

\int 6 x d x

derivative f(x)=(x^3+2x^2-4)/3

d er i v a t i v e f (x) = \frac{x ^{3} + 2 x ^{2} - 4}{3}

integral of (x^2+1)e^{x^3+3x}

\int (x^{2} + 1) e^{x^{3} + 3 x} d x