1. sin^-1 √[x/(x+a)] dx

2. (sin^-1 √x - cos^-1 √x)/ ??(sin^-1 √x + cos^-1 √x) dx

3. tan^-1 {[√(1+x) - √(1-x)]/[√(1+x) + √(1-x)]} dx

1. substitute x=a.tan^2t, then solving u get a simplified expression as follows...........(after writing t again in terms of x)

  = int [tan^-1sqrt(x/a)]dx.......................(1)

now put sqrt(x)=t

substitute value of dx in (1) n use byparts........

3. put x=sint..............this will help to get rid of roots.........

then u get an expression as,

1/2 int[sin^-1(x)]dx

use byparts..................