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Question
If `int (log "x")^2/"x" "dx" = (log "x")^"k"/"k" + "c"`, then the value of k is:
Options
3
2
1
None of the above options
Solution
3
Explanation:
Given, `int (log "x")^2/"x" "dx" = (log "x")^"k"/"k" + "c"`
Taking L.H.S. = `int (log "x")^2/"x" "dx"`
Let, log x = t
∴ `1/"x" "dx" = "dt"`
= `int "t"^2"dt" = "t"^3/3 + "c"`
Substituting the value of t,
= `(log "x")^3/3 + "c"`
On comparing with R.H.S. we get
k = 3
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