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Obtain reduction formula for If I(n)...

Obtain reduction formula for
If ` I_(n)=int (log x) ^(n)dx,` then show that
`I_(n) =x (log x)^(n) -nI_(n-1),` and hence field ` int (log x) ^(4) dx.`

Text Solution

Verified by Experts

The correct Answer is:
`x [(log x)^(4) - 4 (log x)^(3) + 12 (log x)^(2) - 23 log x + 24 ] + c `
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