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int(dx)/(sqrt((1-x)(x-2))) is equal to...

`int(dx)/(sqrt((1-x)(x-2)))` is equal to

A

`sin^(-1)(2x-3)+C`

B

`sin^(-1)(2x+5)+C`

C

`SIN^(-1)(3-2X)+C`

D

`sin^(-1)(5-2x)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `I=int(dx)/(sqrt((1-x)(x-2)))`
`=int(dx)/(sqrt(-x^(2)+3x-2))int(dx)/(sqrt((1)/(4)-(x-(3)/(2))^(2)))`
`=sin^(-1)(((x-(3)/(2)))/((1)/(2)))+C=sin^(-1)(2x-3)+C`
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