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Beliebt Rechnen >

integral of x^4ln^2(x)

Lösung

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

Lösung

\frac{1}{5} x^{5} ln^{2} (x) - \frac{2}{5} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{5} x^{5} ln^{2} (x) - \int \frac{2}{5} x^{4} ln (x) d x

\int \frac{2}{5} x^{4} ln (x) d x = \frac{2}{5} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

= \frac{1}{5} x^{5} ln^{2} (x) - \frac{2}{5} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} x^{5} ln^{2} (x) - \frac{2}{5} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}) + C

Graph

Beliebte Beispiele

derivative of (4x/(x+4))

\frac{d}{d x} (\frac{4 x}{x + 4})

tangent y=8+5x^2-2x^3

t an g e n t y = 8 + 5 x^{2} - 2 x^{3}

inverselaplace (4s)/((s+2)^2)

in v erse l a pl a ce \frac{4 s}{( s + 2 ) ^{2}}

\frac{d}{d y} (\frac{x}{y})

integral from 0 to pi/(12) of tan(6x)

\int_{0}^{\frac{π}{12}} tan (6 x) d x