Hey i have this integral √1+y^2-(cothφ)ydy(with the square root on consisting of 1+y^2. I evaluated it but I just wanna you guys to check and see if you think its good. For the radical part I used a trig substitution y=tanφ The integral of tanφ is ln |sec x| And for the (cothφ)y part I figured it would just be (cothφ)y^2/2 because the function is in terms of dy and I figured I just integrate with respect to y. So this gives me the final answer ln |sec x|-(cothφ)y^2/2 for my final. Does this look good to you guys? My only concern about this is since my y=tanφ would I have to substitute it for the the y after the cothφ? Or I might be thinking of this completely wrong. Need advice!!