Let us consider the integral of the following forms
`f(x_(1), sqrt(mx^(2)+nx+p))^(1//2)`
Case I If `m gt 0`, then put `sqrt(mx^(2)+nx+C)=u pm x sqrt(m)`
Case II If `p gt 0`, then put `sqrt(mx^(2)+nx+C)=u x pm sqrt(p)`
Case III If quadratic equation `mx^(2)+nx+p=0` has real roots `alpha` and `beta` there put `sqrt(mx^(2)+nx+p)=(x-alpha) u ` or `(x-beta)u`
To evaluate `int(dx)/((x-1)sqrt(-x^(2)+3x-2))` one of the most suitable substitution could be

Options

A. `sqrt(-x^(2)+3x-2)=u`
B. `sqrt(-x^(2)+3x-2)=(uxsqrt2)`
C. `sqrt(-x^(2)+3x-2)=u(1-u)`
D. `sqrt(-x^(2)+3x-2)=u(x-2)`

Answer

D