The acid strength of saturated aliphatic carboxylic acids depends mainly upon the inductive effect of the substituent and its position w.r.t. the -COOH group. Where as electron donating substituents tend to increase the acid strength. The acidic strength of aromatic carboxylic acids, on the other hand, depends upon both the inductive and the resonance effect of the substituents.

The pK_a of aspirin is 3.5. The pH of gastric juice in human stomach is about 2-3 and pH in the small intestine is about 8. Aspirin will be:

Ionized in the small intestine  and almost unionized in the stomach. 

Since the pH in the small intestine is about 8 (basic), aspirin is completely ionized here and further since the pH in the stomach is 2-3 (highly acidic), therefore, aspirin which is a weak acid is completely unionized here.