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प्रश्न
Integrate the functions:
`((x+1)(x + logx)^2)/x`
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उत्तर
Let `I = int ((x + 1) (x + log x)^2)/x dx`
`= int (x + log x)^2 (1 + 1/x) dx`
Put x + log x = t
⇒ `(1 + 1/x) dx = dt`
∴ `I = int t^2 dt = t^3/3 + C`
`= 1/3 (x + log x)^3 + C`
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