1.

If intsqrt((x-5)/(x-7))dx=Asqrt(x^(2)-12x+35) +log|x-6+sqrt(x^(2)-12x+35)|+C, then A=

Answer»

`-1`
`(1)/(2)`
`-(1)/(2)`
1

Solution :Let `l=sqrt((X-5)/(x-7))DX`
`=intsqrt(((x-5)(x-5))/((x-7)(x-5)))dx` [rationalising]
`=INT(x-5)/(sqrt(x^(2)-5x-7x+35))dx`
`=int(x-5)/(sqrt(x^(2)-12x+25))dx`
`=(1)/(2)int(2x-10)/(sqrt(x^(2)-12x+35))`
`=(1)/(2)int(2x-12+2)/(sqrt(x^(2)_12x+35))dx`
`=(1)/(2)int(2x-12)/(sqrt(x^(2)-12x+35))dx+int(1)/(sqrt(x^(2)-12x+35))dx`
`=sqrt(x^(2)-12x+35)+int(1)/(sqrt(x^(2)-12x+36-1))dx+C`
`[because" let "x^(2)-12x+35=timplies(2x-12)dx=dt]`
`sqrt(x^(2)-12x+35)+int(1)/(sqrt((x-6)^(2)-1^(2)))dx+c`
`l=sqrt(x^(2)-12x+35)log+|x-6+sqrt(x^(2)-12x+35)|+C`
`thereforel=Asqrt(x^(2)-12x+35)+log|x-6+sqrt(x^(2)-12+35)+C`
`=1*sqrt(x^(2)-12x+35)log|x-6+sqrt(x^(2)-12x+35)+C`
On COMPARING both sides, we get A=1


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