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Beliebt Rechnen >

integral of ((3ln(x)-5)^4)/x

Lösung

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

Lösung

(3 ln (x) - 5)^{4} - 216 ln^{4} (x) - 2100 ln^{2} (x) + \frac{81}{5} ln^{5} (x) + 990 ln^{3} (x) + 2125 ln ∣ x ∣ + C

Schritte zur Lösung

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

Wende die partielle Integration an

= (3 ln (x) - 5)^{4} - \int \frac{12 ( 3 ln ( x ) - 5 ) ^{3} - ( 3 ln ( x ) - 5 ) ^{4}}{x} d x

\int \frac{12 ( 3 ln ( x ) - 5 ) ^{3} - ( 3 ln ( x ) - 5 ) ^{4}}{x} d x = 216 ln^{4} (x) + 2100 ln^{2} (x) - \frac{81}{5} ln^{5} (x) - 990 ln^{3} (x) - 2125 ln ∣ x ∣

= (3 ln (x) - 5)^{4} - (216 ln^{4} (x) + 2100 ln^{2} (x) - \frac{81}{5} ln^{5} (x) - 990 ln^{3} (x) - 2125 ln ∣ x ∣)

Vereinfache

= (3 ln (x) - 5)^{4} - 216 ln^{4} (x) - 2100 ln^{2} (x) + \frac{81}{5} ln^{5} (x) + 990 ln^{3} (x) + 2125 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= (3 ln (x) - 5)^{4} - 216 ln^{4} (x) - 2100 ln^{2} (x) + \frac{81}{5} ln^{5} (x) + 990 ln^{3} (x) + 2125 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of-tan(x)

\int - tan (x) d x

(dy)/(dx)=x^2sqrt(y)

\frac{d y}{d x} = x^{2} y

xy+(x^2+y^2)((dy)/(dx))=0

x y + (x^{2} + y^{2}) (\frac{d y}{d x}) = 0

limit as s approaches-3 of \sqrt[3]{(-4+5s+3s^2)/(-s^3+s+40)}

s \to - 3 lim (3 \frac{- 4 + 5 s + 3 s ^{2}}{- s ^{3} + s + 40})

tangent f(x)=sin(x)

t an g e n t f (x) = sin (x)