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

```

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