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Integrate the functions((1+x)(x+logx)^2)...

Integrate the functions`((1+x)(x+logx)^2)/x`

Text Solution

Verified by Experts

Let I = `int((1+x)(x+logx)^2)/x dx`
= `int(1+1/x)(x+logx)^2)x dx`
= put `x+ logx = t`
diff on both side w.r.t x
`(1+ 1/x )dx = dt`
Hence
`I= int t^2 dt`
= `t^3/3 +c`
...
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