ज्ञात करें ` int sqrt(x/(1-x))dx`

Explanation

`x=sin^2 theta` रखे, तो `dx =2 sin theta cos theta d theta`
अब, `I=intsqrt((sin^2 theta)/(1-sin^2 theta))*2 sin theta cos theta d theta = int 2 (sin theta)/(cos theta)* sin theta cos theta d theta`
`=int 2 sin^2 theta d theta =int (1-cos 2 theta)d theta = theta -(sin 2 theta)/2+c`
`=theta-sin theta cos theta +c = sin^(-1) sqrtx -sqrtxsqrt(1-x)+c`