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Mathomatic version 16.0.5
1−> a=b+1/b
#1: a = b + (1/b)
1−> solve verify b
Solving equation #1 for b with verification...
#1: b = (a - (((a^2 - 4)^(1/2))*sign))/2
All solutions verified.
1−> a ; quick solve
#1: a = (b^2 + 1)/b
1−> simplify
#1: a = b + (1/b)
1−> derivative
Differentiating the RHS with respect to b and simplifying...
#2: a' = 1 - (1/b^2)
2−> integrate b
Integrating the RHS with respect to b and simplifying...
#3: a = b + (1/b)
3−> 
End of input.