Evaluate the following integrals: `intsin^(-1)sqrt(x)dx`

1.	Evaluate the following integrals: `intsin^(-1)sqrt(x)dx`
Answer» Correct Answer - `(1)/(2)(2x-1)sin^(-1)sqrt(x)+(1)/(2)sqrt(x(1-x))+C` Put `sqrt(x)=sint."Then",x=sin^(2)t anddx=sin"2t dt"`. `I=inttsin"2t dt"=-(1)/(2)t cos2t+(1)/(4)sin2t+C` `=(1)/(2)t(2sin^(2)t-1)+(1)/(2)sintcost=(1)/(2)sin^(-1)sqrt(x)(2x-1)+(1)/(2)sqrt(x(1-x))+C`.

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