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Question
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Options
`2sqrt(1 - x) + "c"`
`-2sqrt(1 - x) + "c"`
`sqrtx + "c"`
x + c
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Solution
The value of `int ("d"x)/(sqrt(1 - x)) "is" underlinebb(-2sqrt(1 - x) + c)`.
Explanation:
`int ("dx")/(sqrt(1 - x)) = int(1 - x)^((-1)/2)"dx"`
= `((1 - x)^((-1)/(2 + 1)))/(1/2) xx 1/("d"/("dx") (1 - x)) + "c"`
= `-2(1 - x)^(1/2) + "c"`
= `-2 sqrt(1 - x) + "c"`
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