Mathematica gives bad integral ??

*To*: mathgroup at smc.vnet.net*Subject*: [mg24293] Mathematica gives bad integral ??*From*: "J.R. Chaffer" <jrchaff at mcn.net>*Date*: Fri, 7 Jul 2000 00:11:33 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, this newbie gets erroneous results with Mathematica 4.0 (for students), with the following integral. Hopefully someone can tell me why, and what I may be doing wrong. I have tried "Assumptions -> x e Reals", or x > 0, with same results. Integral in question is, Integrate[1/Sqrt[1-Sin[2x]]] The result is somewhat involved, instead of the expected result (Schaum, "Calculus" 4E, p. 297), integral = - (1/Sqrt[2])Log[Abs[Csc[Pi/4-x]-Cot[Pi/4-x]]] One expects to get differing forms with any computer algebra system, since there are so many equivalent forms of algebraic expressions. However, Mathematica's form and the Schaum (correct) form differ by significant numerical values, as plotting shows (i.e., not some E-16 or some such). Further, and what really seems wrong, is that when one differentiates Mathematica's result for the integral, one does NOT get the original integrand, or anything even close, numerically. So, I am confused. Anyone who knows the explanation would be welcome to share it. Thank you. John Chaffer