Question

`int(logx)^2dx` equals ______.

Options

• (x logx)² – 2x logx + 2x + c

• x(logx)² – 2x logx + 2x + c

• x(logx)² + 2x logx + 2x + c

• x(logx)² + 2x logx – 2x + c

Answer 1

`int(logx)^2dx` equals `underlinebb(x(log x)^2 - 2x log x + 2x + c)`.

Explanation:

I = `int1.(logx)^2dx`  ...[Using by parts]

Take 1 as the second function then,

I = `x(logx)^2 - intx.(2logx)/xdx`

= `x(logx)^2 - 2intlogxdx`

Again by parts

I = `x(logx)^2 - 2[xlogx - intx. 1/x dx]`

= x(logx)² – 2x logx + 2x + c