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Question: How can this be???

Question:How can this be???

william budd 268 Maple
calculus integral infinity
June 21 2007
0
Unless calculus has changed, when evaluating a definite integral, i.e., one with limits, first one performs the integration on the expression and then one evaluates the result for the upper limit and subtracts the result evaluated for the lower limit. That of course means that the indefinite integral (without limits) has to be produced before evaluating the result using the limits. Considering that, here is the confusing situation I have run into. Maple returns an answer, complicated to be sure, but an answer to int(sin(x)*sin(x^3+x), x = 0 .. infinity) suggesting that it CAN integrate sin(x)*sin(x^3+x) but then when I enter int(sin(x)*sin(x^3+x), x) Maple won't perform the integration now suggesting that it CANNOT integrate sin(x)*sin(x^3+x). What is going on here? (Thanks for reading and considering this problem.)
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