माना `x=tanthetarArrdx=sec^2d theta`
`:. intsin^(-1).(2x)/(1+x^2)dx=intsin^(-1)((2tantheta)/(1+tan^2theta))sec^2thetad theta`
`=intsin^(-1)(sin2theta)sec^2thetad theta=int2thetasec^2thetad theta`
`=2[theta.tantheta-int1 tanthetad theta]`
`=2[thetatantheta-logsectheta]+c`
`=2[xtan^(-1)x-logsqrt(1+x^2)]+c`
