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evaluate the indicated integral (lnx+2)^2/x dx

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tarfa | Student, Undergraduate | (Level 3) eNoter

Posted June 8, 2012 at 11:37 AM via web

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evaluate the indicated integral (lnx+2)^2/x dx

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thilina-g | College Teacher | (Level 1) Educator

Posted June 8, 2012 at 12:03 PM (Answer #1)

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`y = int(ln(x)+2)^2/xdx`

Let `u = ln(x)` , then,

`du = 1/x dx`

Then the integral changes into,

`y = int(u+2)^2du`

This gives,

`y = (u+2)^3/3 +c `

Where c is an arbitrary constant.

Replacing u,

`y = (ln(x)+2)^3/3 + c`

 

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