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Beliebt Rechnen >

integral of (ln(y))^2y

Lösung

\int (ln (y))^{2} y d y

Lösung

\frac{1}{2} y^{2} ln^{2} (y) - \frac{1}{2} y^{2} ln (y) + \frac{y ^{2}}{4} + C

Schritte zur Lösung

\int (ln (y))^{2} y d y

Wende die partielle Integration an

= \frac{1}{2} y^{2} ln^{2} (y) - \int y ln (y) d y

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

= \frac{1}{2} y^{2} ln^{2} (y) - (\frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4})

Vereinfache

= \frac{1}{2} y^{2} ln^{2} (y) - \frac{1}{2} y^{2} ln (y) + \frac{y ^{2}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} y^{2} ln^{2} (y) - \frac{1}{2} y^{2} ln (y) + \frac{y ^{2}}{4} + C

Graph

Beliebte Beispiele

derivative (x^2+4)/(x^2-4)

d er i v a t i v e \frac{x ^{2} + 4}{x ^{2} - 4}

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\frac{d}{d x} (- \frac{3}{8 x ^{\frac{5}{2}}})

integral of sec^2(5x)+e^{x/2}

\int sec^{2} (5 x) + e^{\frac{x}{2}} d x

integral of (x^2+1)/(x^2+x-2)

\int \frac{x ^{2} + 1}{x ^{2} + x - 2} d x