# Double integration of a complex function **URL:** \ **Category:** Questions\ **Tags:** calculus\ **Created:** [July 30, 2024, 7:20pm UTC](https://community.wolfram.com/t/double-integration-of-a-complex-function/24373 "2024-07-30T19:20:40Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![orpitasaha](https://avatars.discourse-cdn.com/v4/letter/o/e36b37/32.png) [@orpitasaha](https://community.wolfram.com/u/orpitasaha)\ **Post date:** [July 30, 2024, 7:20pm UTC](https://community.wolfram.com/t/double-integration-of-a-complex-function/24373/1 "2024-07-30T19:20:40Z")
Hi, I want to do the double integration of the following function: ``` Integrate[(-1)*(x + l/2)/((x + l/2)^2 + (y - y1)^2 + (z - z1)^2)^(3/2),{y1, 1,2},{z1,3,4}] ``` But, I am not getting any results. Mathemetica is saying the following things "This computation has exceeded the time limit for your plan.\ ``` $Aborted. ``` I have attached the screenshot of this here. Any suggestions regarding solving this complex double integral will be appreciated. Thanks. ![mathematica error.png](https://global.discourse-cdn.com/wolfram/original/3X/b/8/b83e7e53f0b31c5bdb3a80ad9a2f120b5cde6bf8.png) ---
**Author:** ![mariuszi28cg](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/mariuszi28cg/32/308_2.png) [@mariuszi28cg](https://community.wolfram.com/u/mariuszi28cg)\ **Post date:** [July 30, 2024, 8:50pm UTC](https://community.wolfram.com/t/double-integration-of-a-complex-function/24373/2 "2024-07-30T20:50:55Z")
Mathematica have trouble to compute this integral: [Open in Wolfram Cloud ↗](https://www.wolframcloud.com/obj/26de4976-b38e-4c9e-a4c0-2935826a3bc6) ---
**Author:** ![orpitasaha](https://avatars.discourse-cdn.com/v4/letter/o/e36b37/32.png) [@orpitasaha](https://community.wolfram.com/u/orpitasaha)\ **Post date:** [July 30, 2024, 9:27pm UTC](https://community.wolfram.com/t/double-integration-of-a-complex-function/24373/3 "2024-07-30T21:27:13Z")
Thank you for being so helpful. After doing the double integration over y1 and z1, I need to do triple integration over x,y and z (dx, dy and dz). I tried to do that. I got output for integration over x but did not get any output over y and z. I am not sure why. It might be low memory or something like that. Another problem: My real limits are y1\_max = 0.0019 and y1\_min = -0.0019, z1\_max = 1.15_10^-5 and z1\_min = -1.15_10^-5. If I use those limits, I can not get any output over integration dz1. I am attaching my pdf files here. Real limits for x, y and z are x\_min = -0.006, x\_max = 0.006 y\_min = -0.0019, y\_max = 0.0019 z\_min = -1.25_10^-04, z\_max = 1.25_10^-4 I really appreciate any help you can provide. Thank you. [real limit complexity.pdf](https://community.wolfram.com/uploads/short-url/jXy16xcG4hSHwnMSfqMBwv7GcC6.pdf) (32.7 KB) [triple integration error.pdf](https://community.wolfram.com/uploads/short-url/nUT5FvGZtMQzs9AVvrrVICNLE8E.pdf) (84.1 KB) ---
**Author:** ![mariuszi28cg](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/mariuszi28cg/32/308_2.png) [@mariuszi28cg](https://community.wolfram.com/u/mariuszi28cg)\ **Post date:** [July 31, 2024, 9:37am UTC](https://community.wolfram.com/t/double-integration-of-a-complex-function/24373/4 "2024-07-31T09:37:31Z")
Your integral is **5D.** Why do you expect that there is a closed form solution? Not all integrals can be expressed in closed form. Probably only way is compute numerically. [Open in Wolfram Cloud ↗](https://www.wolframcloud.com/obj/61f71f60-afb1-4326-981a-6d8c834c656a) ---
**Author:** ![orpitasaha](https://avatars.discourse-cdn.com/v4/letter/o/e36b37/32.png) [@orpitasaha](https://community.wolfram.com/u/orpitasaha)\ **Post date:** [July 31, 2024, 6:35pm UTC](https://community.wolfram.com/t/double-integration-of-a-complex-function/24373/5 "2024-07-31T18:35:00Z")
Thanks. Got it.