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Evaluate the integral `int(p^2)(lnp)dp`
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The integral `int p^2*ln(p) dp` has to be determined.
Let `ln(p) = y => p = e^y` , `p*dy = dp`
`int p^2*ln(p) dp`
=> `int e^(2y)*y*e^y dy`
=> `int e^(3y)*y*dy`
Use integration by parts, let u = y and v = e^(3y)
=> `y*e^(3y) - int e^(3y) dy`
=> `y*e^(3y) - e^(3y)/3`
substitute y = ln(p)
=> `ln(p)*e^(ln p^3) - (e^(lnp^3))/3`
=> `ln(p)*p^3 - p^3/3`
The integral `int p^2*ln(p) dp = ln(p)*p^3 - p^3/3 + C`
Posted by justaguide on February 1, 2013 at 5:18 PM (Answer #1)
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