Repository of functions which do not have elementary integrals
61267
List of functions not integrable in elementary terms
21843
Proving a function is not Riemann integrable
136996
Fourier transform of function composition
44148
Functions that are their own inverse.
87041
How to determine with certainty that a function has no elementary antiderivative?
68171
Non-trigonometric Continuous Periodic Functions
109985
Books/Resources on generating functions
74793
The primitive of a discontinuous function?
68287
Good book on evaluating difficult definite integrals (without elementary antiderivatives)?
118791
Efficient evaluation of functions defined by NIntegrate
12639
Example of primitive function which isn't Riemann-integrable on a closed interval [0,1]
100436
Examples of nowhere continuous functions
20688
Discontinuous functions with closed graphs
103241
A function that is continuous at the origin but not differentiable there
4813
On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?)
134558
Visual references for the Riemann-Stieltjes integral.
54137
Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable