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

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

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` int ((x+1)(x+log x)^(2))/(x)dx " " underset(rArr (1+(1)/(x)) dx=dt)(" Let " x + log x =t)`
`= int t^(2) dt = (1)/(3) t^(3)+c" " rArr ((x+1)/(x)) dx =dt`
`=(1)/(3) (x+ log x)^(3) +c`
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