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int (" In" x)^(-1) dx - int ("In" x)^(-2...

`int (" In" x)^(-1) dx - int ("In" x)^(-2) dx` is equal to

A

`x ("In " x)^(-1) + c`

B

`x("In " x)^(-2) + c`

C

`x(" In "x) +c`

D

`x("In " x)^(2) + c`

Text Solution

Verified by Experts

The correct Answer is:
A
`int (l nx)^(-1) dx - int (l n x)^(-2) dx`
`= int [(1)/(l nx) - (1)/((l nx)^(2))].dx`
Put `l nx = t rArr x = e^(t)`
`dx = e^(t).dt`
`:. int [(1)/(l nx) - (1)/((l nx)^(2))] dx = int ((1)/(t) - (1)/(t^(2))) .e^(t).dt`
`= int e^(t) .((1)/(t) - (1)/(t^(2))) .dt`
`= (e^(t))/(t) + c = (x)/(l nx) + c`
`= x(l nx)^(-1) + c`
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