The integral of -2x/(2x - 1)^3 is x^2/(2x - 1)^2, we have to find the integral of 4x-3/(2x-1)^3
4x-3/(2x-1)^3
=> 4x/(2x - 1)^3 - 3/(2x - 1)^3
=> -2*(-2x/(2x - 1)^3 - 3/(2x - 1)^3
`int (-2*-2x)/(2x - 1)^3 dx -int 3/(2x - 1)^3 dx`
=> `(-2*x^2)/(2x - 1)^2 - int 3/(2x - 1)^3 dx`
let 2x - 1 = t => dt = 2*dx => 3*dx = (3/2) dt
=> `(-2x^2)/(2x - 1)^2 - (3/2)*int 1/(t^3) dt`
=> `(-2x^2)/(2x - 1)^2 - (3/2)/(-2*t^2)`
substitute t = 2x - 1
=> `(-2x^2)/(2x - 1)^2 + 3/(4*(2x - 1)^2)`
The required integral is `((3/4) - 2x^2)/(2x - 1)^2 + C`
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