erweitern x^{1/x-2}*(1-ln(x))

Lösung

erweitern

x^{\frac{1}{x} - 2} \cdot (1 - ln (x))

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

Schritte zur Lösung

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

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = x^{\frac{1}{x} - 2}, b = 1, c = ln (x)

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

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

Multipliziere:

1 \cdot x^{\frac{1}{x} - 2} = x^{\frac{1}{x} - 2}

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

e x p an d \frac{5 - x}{x ( x - 3 )}

e x p an d (2 x + 7)^{2} π

e x p an d \frac{1}{s ( s + a ) ( s + b )}

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

e x p an d (k + 1)! \cdot (k + 2) - 1