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प्रश्न
Evaluate the following.
`int 1/("x" log "x")`dx
उत्तर
Let I = `int 1/("x" log "x")`dx
Put log x = t
∴ `1/"x" "dx" = "dt'`
∴ I = `int 1/"t"` dt = log |t| + c
∴ I = log |log x| + c
Alternate Method:
Let I = `int 1/("x" * log "x")`dx
`= int (1//"x" "dx")/(log "x")`
∴ I = log |log x| + c .....`[because int ("f" '("x"))/("f"("x")) "dx" = log |"f"("x")| + "c"]`
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