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

Lösung

erweitern

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

\frac{1}{x ^{5} + 2 x ^{3} + x + x ^{4} + 2 x ^{2} + 1}

Schritte zur Lösung

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

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

= \frac{1}{( x + 1 ) ( x ^{4} + 2 x ^{2} + 1 )}

Multipliziere aus

(x + 1) (x^{4} + 2 x^{2} + 1) : x^{5} + 2 x^{3} + x + x^{4} + 2 x^{2} + 1

= \frac{1}{x ^{5} + 2 x ^{3} + x + x ^{4} + 2 x ^{2} + 1}

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

e x p an d (2 - \frac{1}{2} x)^{10}

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

e x p an d (- 2 sin (t))^{2} + (2 cos (t))^{2} + (4 cos (t) - 2 sin (t))^{2}

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