माना `i=int sin^(-1) sqrtx dx`
माना `x = sin^(2)theta`
`dx= 2sinthetacostheta d theta`
`dx=sin2thetad theta`
`:. I =intsin^(-1)(sintheta).sin2thetad theta`
`=int theta.sin2theta d theta`
`= thetaintsin2thetad theta-int[d/(d theta)theta.intsin2thetad theta]d theta`
`= [ theta.(-cos2theta)/2]-int1.(-cos2theta)/2d theta`
`=-1/2. thetacos2theta+1/2[(sin2theta)/2]+c`
`=-1/2theta.(1-2sin^2theta)+1/4[2sinthetacostheta]+c`
`=-1/2sin^(-1)sqrtx.(1-2sin^2theta)+1/4[2sqrtxsqrt(1-x)]+c` [`theta` का मान रखने पर]
`=-1/2sin^(-1)sqrtx+x.sin^(-1)sqrtx+1/2sqrtxsqrt(1-x)+c`
`=xsin^(-1)sqrtx-1/2[sin^(-1)sqrtx-sqrtxsqrt(1-x)]+c`
