erweitern (1+ln(x))/(x^2(1-ln(x))^3)

Lösung

erweitern

\frac{1 + ln ( x )}{x ^{2} ( 1 - ln ( x ) ) ^{3}}

\frac{1 + ln ( x )}{x ^{2} - 3 x ^{2} ln ( x ) + 3 x ^{2} ln ^{2} ( x ) - x ^{2} ln ^{3} ( x )}

Schritte zur Lösung

\frac{1 + ln ( x )}{x ^{2} ( 1 - ln ( x ) ) ^{3}}

(1 - ln (x))^{3} = 1 - 3 ln (x) + 3 ln^{2} (x) - ln^{3} (x)

= \frac{1 + ln ( x )}{x ^{2} ( 3 ln ^{2} ( x ) - ln ^{3} ( x ) - 3 ln ( x ) + 1 )}

Multipliziere aus

x^{2} (1 - 3 ln (x) + 3 ln^{2} (x) - ln^{3} (x)) : x^{2} - 3 x^{2} ln (x) + 3 x^{2} ln^{2} (x) - x^{2} ln^{3} (x)

= \frac{1 + ln ( x )}{x ^{2} - 3 x ^{2} ln ( x ) + 3 x ^{2} ln ^{2} ( x ) - x ^{2} ln ^{3} ( x )}

e x p an d \frac{( x - 3 ) ( x + 6 )}{x + 7}

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

e x p an d (y^{- 1})^{4}

e x p an d - \frac{( 6 x - 5 )}{( 3 x ^{2} - 5 x + 7 ) ^{2}}

\frac{\partial}{\partial x} ((y) (x - y))