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Hot answers tagged numerical-integration

7

Update Almost ten times faster again, or about 90 times faster than the OP's way (0.069 sec v. 5.46 sec): For the second integral, we can find its derivative with respect to x and then integrate with NDSolve. The derivative of the integral has two components, one from differentiating under the integral sign dxdz1 and one from plugging in the limit of ...

4

Put assumptions in: Clear[a, c] Integrate[ q^2 ((4 (c π))/((a q^2 - c) (c + a q^2))), {q, 0, ∞}, Assumptions -> {a, c} ∈ Reals] (* ConditionalExpression[(Sqrt[c] π^2)/a^(3/2), (a > 0 && c > 0) || (a < 0 && c < 0)] *)

3

The exact analytic soultion 1. Introduction The problem was still intriguing me with the result of a further study which I present in the following, for clarity as another solution. I have chosen to write the formulas in the more theoretical text in traditonal form. Abstract We calculate here the explcit analytic solution for the integral \$f(k,R)=\int ...

1

Just to add a couple of more observations to Nasser's. Case 6 As Daniel Lichtblau hints at in a comment, if we use an exact 37/10 in place of the approximate 3.7, we get an exact result with a zero imaginary component: Integrate[PDF[NormalDistribution[14, 37/10], x], {x, 15, Infinity}] N@% (* 1/2 Erfc[(5 Sqrt[2])/37] 0.393476 *) Case 7 Such a small ...

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