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

Answer 1

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