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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Multipliziere aus

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

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

e x p an d \frac{( - 3 y + 3 d + 2 ) ^{2}}{16}

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

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

e x p an d e x p an (1 + 4 x)^{7}

e x p an d (x - 2) (y^{2} + 25) d x