2
$\begingroup$

I need to integrate the expression G given below:

R = {Rx, Ry, Rz}; b = {bx, by, bz}; r = Sqrt[(s*b - R).(s*b - R)]; K = Exp[-r/L]/r; G = Simplify[-K*(1/r + 1/L)*1/r*b.(s*b - R)];

If I use:

Integrate[G,{s,0,1}]

it takes quite a long time; instead if I use:

int = Integrate[G, s] Simplify[(int /. s -> 1) - (int /. s -> 0)]

it takes less than a second.

Why is it so?

Improve this question
$\endgroup$
1

1 Answer 1

Reset to default
4
$\begingroup$

When calculating indefinite integrals Mathematica does not care about the convergence in a domain {x_min,x_max}. In case of definite integrals, at times it is necessary to provide information on the constants in order to obtain the proper result. Check the tutorial on definite integrals. The example with 1/(1 + a Sin[x]) is very similar to your problem.

Improve this answer
$\endgroup$
1
  • 4
    $\begingroup$ Since this is a fine answer (and I upvoted) I'll post this as a comment. One can often get improvements by giving assumptions and/or requesting that no conditions be generated. In this example that might be something like Integrate[G, {s, 0, 1}, GenerateConditions -> False, Assumptions -> {Thread[Variables[G] > 0]}] $\endgroup$ Commented Apr 29, 2014 at 15:07

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.