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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. 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..................
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