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Beliebt Rechnen >

integral of xln^2(5x)

Lösung

\int x ln^{2} (5 x) d x

Lösung

\frac{1}{2} x^{2} ln^{2} (5 x) - \frac{1}{2} x^{2} ln (5 x) + \frac{x ^{2}}{4} + C

Schritte zur Lösung

\int x ln^{2} (5 x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} ln^{2} (5 x) - \frac{1}{2} x^{2} ln (5 x) + \frac{x ^{2}}{4} + C

Graph

Beliebte Beispiele

integral of 2x+3y

\int 2 x + 3 y d x

derivative f(x)=2sqrt(x)-1/(2sqrt(x))

d er i v a t i v e f (x) = 2 x - \frac{1}{2 x}

f(x)=7x^3+7x^2+7x+3

f (x) = 7 x^{3} + 7 x^{2} + 7 x + 3

derivative of (x^4-1^3(x^3+1)^4)

\frac{d}{d x} ((x^{4} - 1)^{3} (x^{3} + 1)^{4})

tangent f(x)=x^2-1,\at x=0

t an g e n t f (x) = x^{2} - 1, at x = 0