Question

`int (logx)^2/x dx` = ______.

Options

• `(logx/x)^3 + C`

• `(logx/3)^3 + C`

• `(logx)^3/2 + C`

• `(logx)^3/3 + C`

Answer 1

`int (logx)^2/x dx` = `underlinebb((logx)^3/3 + C)`

Explanation:

Let I = `int (log x)^2/x  dx`

Put log x = t

`\implies 1/x dx` = dt

∴ I = `int (log x)^2/x  dx`

= `int t^2 dt`

= `t^3/3 + C`  ...[put t = logx]

= `(log x)^3/3 + C`