What is partialfraction (x^3)/(x^2-1) ?

The solution to partialfraction (x^3)/(x^2-1) is x+1/(2(x+1))+1/(2(x-1))

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partialfraction (x^3)/(x^2-1)

partial fractions

\frac{x ^{3}}{x ^{2} - 1}

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

Solution steps

\frac{x ^{3}}{x ^{2} - 1}

Long division

\frac{x ^{3}}{x ^{2} - 1} : x + \frac{x}{x ^{2} - 1}

= x + \frac{x}{x ^{2} - 1}

Continue partial fractions on remainder:

\frac{x}{x ^{2} - 1}

Take the partial fraction of

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

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

k = 1 \sum \infty 0. 5^{k}

\int \frac{1}{4096} cos (8 x) d x

\frac{e ^{- 2 s}}{s - 1}

\frac{d y}{d t} = \frac{2}{t} y + t^{3} e^{t}

What is partialfraction (x^3)/(x^2-1) ?
The solution to partialfraction (x^3)/(x^2-1) is x+1/(2(x+1))+1/(2(x-1))