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Originally Posted by Qfwfq
That doesn't show what you said, that "the rest is just algebraic manipulation".
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Sure it does, in the sense that the answer is arrived at mechanically in a finite number of steps by following a specific algorithm.
Quote:
Originally Posted by Qfwfq
Neither does it disprove what I said. Even substitution and by parts are not always simple to apply, tricks may be needed and some of these are not algebraic manipulation (especially when even the functions involved are not algebraic). A cleverly written algorithm might incorporate all known tricks and computers are good at trying all possibilities without loosing track or forgetting some of them, so that doesn't mean that it's easy.
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I don't recall having to integrate anything in lower division calculus that was outside of the usual routine process. Perhaps you need to find an example from baby calculus where doing an integral requires more than obvious substitution or integration by parts.
