- #1

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[tex]\int[/tex]ln

^{2}|x|dx (from -1 to 1)

what i did was integration in parts

[tex]\int[/tex]ln

^{2}|x|dx =x*ln

^{2}|x| - [tex]\int[/tex]2(lnx/x)xdx

=x*ln

^{2}|x| - 2[xln|x| - x]

=lim x(ln

^{2}|x|-2ln|x|+ 2)|[tex]^{-1}_{0-\epsilon}[/tex] +(ln

^{2}|x|-2ln|x|+ 2)|[tex]^{0+\epsilon}_{1}[/tex]

[tex]\epsilon[/tex]->0

1st of all is this correct,?

2nd of all, is there no better way to solve this