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For x lt 1, int (x-x^2)/(sqrt(1-x))dx=...

For `x lt 1, int (x-x^2)/(sqrt(1-x))dx=`

A

`4/3 (1-x)^(3//2)-2/5(1-x)^(5//2)-2sqrt(1-x)+C`

B

`4/3(1-x)^(3//2)-2/3(1-x)^(5//2)-2sqrt(1-x)+C`

C

`2/3(1-x)^(3//2)-2/3(1-x)^(5//2)-2 sqrt(1-x)+C`

D

`-2/15(1-x)^(3//2)(2+3x)+C`

Text Solution

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The correct Answer is:
D
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