erweitern ((x-1)/2)^x(ln((x-1)/2)+x/(x-1))

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

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

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

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

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

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

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

s im pl i f y (1 + x^{2}) (1 + x^{2} + x)

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

s im pl i f y (- 1 - i 3)^{10}

s im pl i f y (x + i y)^{8}