Evaluate: `inttan^(-1)sqrt((1-x)/(1+x))dx`

Explanation

`" Let " I= int tan^(-1) sqrt((1-x)/(1+x))dx`
`" Let " x=cos 0 rArr dx=- sin 0d0`
`I= int tan^(-1) sqrt((1=cos0)/(1+cos0))(-sin 0)d0`
`=int tan^(-1) sqrt((2sin^(2)((0)/(2)))/(2cos^(2)((0)/(2))))(-sin0)d0`
`=int tan^(-1) (tan.(0)/(2)) (-sin 0)d0`
` =(1)/(2) int_(1)^(0)(-underset(II)(sin)0)d0`
` =(1)/(2) {0cos0- int 1 cos 0 d0}+C`
`=(1)/(2) 0 cos 0 -(1)/(2) sin0+C`
`=(1)/(2) (cos^(-1) x)x-(1)/(2) sqrt(1-cos^(2)0)+C`
`=(1)/(2) x cos^(-1) x-(1)/(2) sqrt(1-x^(2))+C`