Besides the suggestions below, it is instructive to go to the math stackexchange and look at the highest voted Q&As tagged 'integrals' or 'definite-integrals'.

Besides the suggestions below, it is instructive to go to the math stackexchange and look at the highest voted Q&As tagged 'integrals' or 'definite-integrals'. Legends like Cleo lurk there demonstrating mind-boggling feats of integration. The corresponding mathoverflow tags are also interesting, but likely to involve more advanced concepts.