What is expand 1/(x(1-ln(x))^2) ?

The solution to expand 1/(x(1-ln(x))^2) is 1/(x-2xln(x)+xln^2(x))

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expand 1/(x(1-ln(x))^2)

expand

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

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

Solution steps

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

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

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

Expand

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

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

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

(x - 1) ln (x)

(x^{2} + y^{2}) d x - x y d y

(x + d x)^{2}

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

What is expand 1/(x(1-ln(x))^2) ?
The solution to expand 1/(x(1-ln(x))^2) is 1/(x-2xln(x)+xln^2(x))