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Let us consider the integral of the foll...

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

A

`sqrt(9x^(2)+4x+6)=upm3x`

B

`sqrt(9x^(2)+4x+6)=3upmx`

C

`x=(1)/(t)`

D

`9x^(2)+4x+6=(1)/(t)`

Text Solution

Verified by Experts

The correct Answer is:
A
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