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Integrate the following w.r.t.x. (logx...

Integrate the following w.r.t.x.
`(logx)^(2)`

Text Solution

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`int (log x)^(2)dx=int (log x)^(2).(1)dx=(log x)^(2)int 1dx-int [(d)/(dx)(log x)^(2).int 1dx]dx`
`=(log x)^(2)-int (2logx)/(x).(x)dx=x (log x)^(2)-2(log x)(1)dx`
`=x (log x)^(2)-2{(log x) f 1dx-int [(d)/(dx)(log x)int 1dx]dx}`
`=x (log x)^(2)-2(log x)(x)+2int (1)/(x).xdx`
`=x(log x)^(2)-2x log x+2int 1 dx`
`=x (log x)^(2)-2xlogx+2x+c=x[(log x)^(2)-2logx+2]+c`
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