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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

e x p an d \frac{d}{d x} ((x + 6) (2 x^{2} + 4 x)) + 3

e x p an d \frac{5}{x + 1} + \frac{( 3 x - 1 )}{x ^{2} + x + 1}

e x p an d (- e^{2 t} sin (t) + e^{2 t} cos (t))^{2}

e x p an d \frac{3 ( x ^{2} - 9 x + 20 )}{2}

e x p an d (x^{2} - 5 e x + 3) (x^{3} + 2 x + 1)