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intxsqrt(1+x-x^(2))dx...

`intxsqrt(1+x-x^(2))dx`

A

`(1)/(3)sqrt((1+x-x^2)^3)+(1)/(16)((2x-1)sqrt(1+x-x^2)+(5)/(2)sin^(-1)((2x-1)/(sqrt(5))))+c`

B

`(1)/(3)sqrt((1+x-x^2)^3)-(1)/(16)((2x-1)sqrt(1+x-x^2)+(5)/(2)sin^(-1)((2x-1)/(sqrt(5))))+c`

C

`(-1)/(3)sqrt((1+x-x^2)^3)-(1)/(8)((2x-1)sqrt(1+x-x^2)+(5)/(2)sin^(-1)((2x-1)/(sqrt(5))))+c`

D

`(-1)/(3)sqrt((1+x-x^2)^3)+(1)/(8)((2x-1)sqrt(1+x-x^2)+(5)/(2)sin^(-1)((2x-1)/(sqrt(5))))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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