#int1/(x^2-12)#?

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#int1/(x^2-12)dx#?

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Answer 1 · 2018-02-23T05:19:26

# sqrt3/12ln|(x-2sqrt3)/(x+2sqrt3)|#.

Let, #I=int1/(x^2-12)dx=int1/{(x-2sqrt3)(x+2sqrt3)}dx#,

#=1/(4sqrt3)int(4sqrt3)/{(x-2sqrt3)(x+2sqrt3)}dx#,

#=1/(4sqrt3)int{(x+2sqrt3)-(x-2sqrt3)}/{(x-2sqrt3)(x+2sqrt3)}dx#,

#=1/(4sqrt3)int{(x+2sqrt3)/{(x-2sqrt3)(x+2sqrt3)}-(x-2sqrt3)/{(x-2sqrt3)(x+2sqrt3)}}dx#,

#=1/(4sqrt3)int{1/(x-2sqrt3)-1/(x+2sqrt3)}dx#,

#=1/(4sqrt3){ln|(x-2sqrt3)|-ln|(x+2sqrt3)|}#,

#=1/(4sqrt3)ln|(x-2sqrt3)/(x+2sqrt3)|#.

# rArr I=sqrt3/12ln|(x-2sqrt3)/(x+2sqrt3)|#.

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