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Beliebt Rechnen >

integral of ln^5(x)

Lösung

\int ln^{5} (x) d x

Lösung

x ln^{5} (x) - 5 (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^{5} (x) d x

Wende die partielle Integration an

= x ln^{5} (x) - \int 5 ln^{4} (x) d x

\int 5 ln^{4} (x) d x = 5 (x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))))

= x ln^{5} (x) - 5 (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^{5} (x) - 5 (x ln^{4} (x) - 4 (x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)))) + C

Graph

Beliebte Beispiele

limit as x approaches 10+of 1/((x-10)^2)

x \to 10 + lim (\frac{1}{( x - 10 ) ^{2}})

integral from-5 to 5 of (x-sqrt(25-x^2))

\int_{- 5}^{5} (x - 25 - x^{2}) d x

derivative of 1/(3+(2x+1^2))

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

cos(t)y^'+sin(t)y-1=0

cos (t) y^{^{'}} + sin (t) y - 1 = 0

tangent f(x)=2sqrt(x),(1,2)

t an g e n t f (x) = 2 x, (1, 2)