There isn't an applied mathematics thread so i'll post this here. I'm an undergraduate and I have a presentation for my numerical methods/matlab class . I'm looking for examples of 1)Integrals which are easier/faster to integrate numerically than do evaluate using their antiderivatives. (power series etc) 2)Integrals whose antiderivatives are not elementary functions on a bounded interval without ''smoothness'' problems on bounds, and if possible with a known integral value. Thank you.