The rate law for the 3rd order reaction of the type *A + B + C* → *P* is:

Using the same logic described in a previous article, we can rewrite the rate law as:

where *a* = [*A _{0}*],

*b*= [

*B*] and

_{0}*c*= [

*C*].

_{0}Integrating the above equation throughout, we have

Substituting the partial fraction expression in the above integral and after some algebra, we have,