ज्ञात करें `int sqrt((1-x)/(1+x)dx`

Explanation

माना की `x=cos 2 theta,` तो `dx = -2 sin 2 theta d theta`
अब, `int sqrt((1-x)/(1+x))dx=int sqrt((1-cos 2 theta)/(1+cos 2 theta))(-2 sin 2 theta)d theta`
`=-2 int (sin theta)/(cos theta) 2 sin theta cos theta d theta = -2 int 2 sin^2 theta d theta`
`=-2 int (-1 cos 2 theta) d theta = - 2[theta - (sin 2 theta)/2]+c`
`=-2 theta + sin 2 theta+c `
`because cos 2 theta = x" ":." "2 theta = coc^(-1)x `
तथा `sin 2 theta =sqrt(1-cos^(2)2 theta)=sqrt(1-x^2)`
अतः (1) से, `int sqrt((1-x)/(1+x))dx=- cos^(-1)x+sqrt(1-x^2)+c`