`sin^(-1)((2x)/(1+x^(2)))`

Explanation

`intsin^(-1).(2x)/(1+x^(2))dx=2 inttan^(-1)x.1 dx`
माना `1+x^(2)=t" "rArr" "2xdx=dt" "rArr" "xdx=(dt)/(2)`
`=2[tan^(-1)x. int 1dx - int {(d)/(dx) tan^(-1)x int 1 dx }dx]`
`=2[x tan^(-1)x-int(x)/(1+x^(2))dx]`
`=2[x tan^(-1)x-int(dt)/(2t)]`
`=2xtan^(-1)x-log t+C`
`=2x tan^(-1)x-log(1+x^(2))+C`