The variables t and x are related by t = x+√(x^2+2bx+c) where b and c are constants and

b^2<c. Show that

dx/dt=(t-x)/(t+b)

and hence integrate

1/√(x^2+2bx+c)

Verify by direct integration that your result holds also in the case b^2 = c if x+b > 0 but that

your result does not hold in the case b^2 = c if x + b < 0 .

[and come someone tell me how to use the math symbols at this site.. i had to do everything in microsoft word ]