No. The issue is existence, not what form it takes. --Dan << Do you mean "have a closed form integral"? If so, f = log(x) and g = e^x gives f'*g = (e^x)/x, which requires a special function to integrate. Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] On Behalf Of James Propp [jpropp@cs.uml.edu] Sent: Tuesday, February 26, 2008 9:13 AM To: math-fun@mailman.xmission.com Subject: Re: [math-fun] functions behaving badly Here's another "dirty secrets of the calculus" question (arising from my preparing to teach integration by parts): If f and g are differentiable, must f'(x) g(x) have an antiderivative? (Note that the product rule implies that if f'(x) g(x) has an antiderivative, then so does f(x) g'(x), and vice versa But it's conceivable to me that there could be cases where neither of the two functions has an antiderivative.) Jim Propp

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele