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

Lösung

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

\int_{1}^{6} t^{4} ln (4 t) d t

\frac{d}{d x} (5 π^{2})

\int x e^{9 x} d x

in v erse l a pl a ce \frac{4 s}{s ^{2} - 16}

\frac{d}{d x} (sin (x + \frac{π}{2}) - cos (x))