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Beliebt Rechnen >

integral of ln(x)*ln(x)

Lösung

\int ln (x) \cdot ln (x) d x

Lösung

x ln^{2} (x) - 2 x ln (x) + 2 x + C

Schritte zur Lösung

\int ln (x) ln (x) d x

Wende die partielle Integration an

= ln (x) (x ln (x) - x) - \int ln (x) - 1 d x

\int ln (x) - 1 d x = x ln (x) - 2 x

= ln (x) (x ln (x) - x) - (x ln (x) - 2 x)

Vereinfache

ln (x) (x ln (x) - x) - (x ln (x) - 2 x) : x ln^{2} (x) - 2 x ln (x) + 2 x

= x ln^{2} (x) - 2 x ln (x) + 2 x

Füge eine Konstante zur Lösung hinzu

= x ln^{2} (x) - 2 x ln (x) + 2 x + C

Graph

Beliebte Beispiele

y^{''}x=-5sin(8x)

y^{^{''}} x = - 5 sin (8 x)

(\partial)/(\partial x)(xln(z^7+x^5))

\frac{\partial}{\partial x} (x ln (z^{7} + x^{5}))

derivative f(x)=(x^2+4x+3)^2

d er i v a t i v e f (x) = (x^{2} + 4 x + 3)^{2}

sum from n=1 to infinity of n/(2^{n-1)}

n = 1 \sum \infty \frac{n}{2 ^{n - 1}}

y^{^{'}} - \frac{1}{x} y = 1