I'm not looking for the solved integrals, I'm just looking for a simple explanation for why
∫cos(x2)dx
is so much more complicated than
∫cos(x)dx
With simple I mean something I can say to explain the difference to a person just starting to learn about integration. Perhaps something visual?
Answer
For one thing, look at their graphs. Since x increases at a constant rate, cos(x) has a constant period but x2 increases faster and faster for larger x so the "period" of cos(x2) keeps getting smaller and smaller.
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