What is the integral of (xln(x))^2(1/(x^2)) ?

The integral of (xln(x))^2(1/(x^2)) is xln^2(x)-2(xln(x)-x)+C

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integral of (xln(x))^2(1/(x^2))

\int (x ln (x))^{2} (\frac{1}{x ^{2}}) d x

x ln^{2} (x) - 2 (x ln (x) - x) + C

Solution steps

\int (x ln (x))^{2} \frac{1}{x ^{2}} d x

Simplify

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

= \int ln^{2} (x) d x

Apply Integration By Parts

: x ln^{2} (x) - \int 2 ln (x) d x

= x ln^{2} (x) - \int 2 ln (x) d x

\int 2 ln (x) d x = 2 (x ln (x) - x)

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

Add a constant to the solution

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

2 x

\int 9 t^{2} + 4 d t

y^{^{'}} = x + y + 1

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

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What is the integral of (xln(x))^2(1/(x^2)) ?
The integral of (xln(x))^2(1/(x^2)) is xln^2(x)-2(xln(x)-x)+C