Definite integral problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg88518] Definite integral problem*From*: UHAP023 at alpha1.rhbnc.ac.uk*Date*: Wed, 7 May 2008 07:08:14 -0400 (EDT)

Dear All, Does anybody know any tricks to do the following definite integral? J0part=(1/Sqrt[const/(Rvt^2 + Rx^2*Sin[theta]^2)^3] + (3*Dc*Sec[theta]^2*(Rvt^2 + Rx^2*Sin[theta]^2)^3)/ (const*Rx^2))^(-1) IntJ0term = Integrate[J0part, {theta, 0, Pi/2}, Assumptions -> {Rx > 0, Rvt > 0, const > 0, Dc > 0}] The integrand seems to be well behaved -- temporarily making some simple numerical substitutions eg. Rx = 1; Rvt = 2; const = 3; Dc = 4; enables it to plotted over the range of the integration limits and also integrated with NIntegrate. Plot[J0part, {theta, 0, Pi/2}] reveals a simple smooth curve. J0part can be split into two partial fractions, neither of which will symbolically integrate. Curiously, different versions of Mathematica and trivially different versions of the integrand get different responses from Integrate[] -- some give up almost immediately, other rack up hours of CPU time without producing a result. Any ideas? Thanks Tom Crane. Ps. I am running Mathematica 4.0. Pps. The email address in the message header is a spam trap only. -- Tom Crane, Dept. Physics, Royal Holloway, University of London, Egham Hill, Egham, Surrey, TW20 0EX, England. Email: T.Crane at rhul dot ac dot uk Fax: +44 (0) 1784 472794