You will translate as in the following:

to differentiate = dériver

to integrate = intégrer

edit: if I look for the meaning of differentiate, the definition match with french dériver (If I dérive f(x) = x^2 I got f'(x)=2x). but if I look for the translation of dériver in maths meaning I got to derive.

Are to differentiate and to derivesynonyms?

The verb "dériver" has two important meanings in mathematics:

1. to obtain the derivative of a function; it’s the translation of "to differentiate" in the present case.

   ex: Si on dérive f(x)=x² on obtient f'(x)=2x.

2. to deduce a mathemetical fact through the use of logical principles and principles of the theory at hand; in other words to prove a theorem or a lemma; it’s then the translation of "to deduce" or "to derive".

ex: On dérive ce théorème à partir des théorèmes 3, 4, et 5 de la section précédente.

3. For the verb "to integrate" there is no other word in French than "intégrer".

ex: Si on intègre la fonction exponentielle on obtient encore la fonction exponentielle.