What is expand (dx)/(x(x^2+1)^2) ?

The solution to expand (dx)/(x(x^2+1)^2) is (dx)/(x^5+2x^3+x)

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expand (dx)/(x(x^2+1)^2)

expand

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

\frac{d x}{x ^{5} + 2 x ^{3} + x}

Solution steps

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

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

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

Expand

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

= \frac{d x}{x ^{5} + 2 x ^{3} + x}

\frac{( 7 x + 10 ) ( x - 1 )}{( x + 1 ) ( 2 x - 17 )}

\frac{- 3 x ^{2} + 4 x - 12}{( 3 x - 2 ) ^{2}}

\frac{( x - 3 ) ( x - 1 )}{( x + 4 ) ( x - 2 )}

\frac{1}{x ( k - x )}

\frac{12 ( x + 1 ) ( x - 1 )}{( x ^{2} + 3 ) ^{3}}

What is expand (dx)/(x(x^2+1)^2) ?
The solution to expand (dx)/(x(x^2+1)^2) is (dx)/(x^5+2x^3+x)