erweitern ln(x)(xln(x)-x)

Lösung

erweitern

ln (x) (x ln (x) - x)

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

Schritte zur Lösung

ln (x) (x ln (x) - x)

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = ln (x), b = x ln (x), c = x

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

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

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

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

e x p an d \frac{2}{( 1 - y ) ( 2 - x - y )}

e x p an d ln (x^{2} + 1) + x^{2} (2 x arctan (x) - 1) 6

e x p an d \frac{( x ^{4} + x )}{x}

e x p an d \frac{( s + 3 ) ( s + 2 )}{( s + 1 ) ( s ^{2} + 2 s + 3 )}

e x p an d \frac{( x ^{2} + 4 ) ^{2}}{( 2 x ^{3} - 1 ) ^{3}}