Timeline for How to integrate this product of Exp[] and Cos[] using Mathematica
Current License: CC BY-SA 4.0
10 events
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| May 16, 2022 at 10:56 | comment | added | user14634 | Thanks a lot for your help! | |
| May 16, 2022 at 10:55 | vote | accept | user14634 | ||
| May 15, 2022 at 3:44 | answer | added | cvgmt | timeline score: 5 | |
| May 14, 2022 at 19:28 | history | edited | MarcoB | CC BY-SA 4.0 |
Removed unreadable formatted form
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| May 14, 2022 at 17:12 | comment | added | Michael E2 |
If you wait, this gives a result with a condition for integrability: Integrate[ Exp[-a x^2 + b x] Cos[x t] // TrigToExp, {x, -Infinity, Infinity}]
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| May 14, 2022 at 16:58 | comment | added | Michael E2 |
Less restrictive assumptions, faster too: res = Integrate[Exp[-a x^2 + b x] Cos[x t] // TrigToExp, {x, -Infinity, Infinity}, Assumptions -> a > 0]. And res // ExpToTrig // TrigExpand // Simplify gives a nice looking result.
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| May 14, 2022 at 16:03 | comment | added | Daniel Huber | Obviously a has to be greater zero, t needs to be real, and there are no restrictions on b. | |
| May 14, 2022 at 15:02 | comment | added | cvgmt |
Integrate[Exp[-a x^2 + b x] Cos[x t], {x, -Infinity, Infinity}, Assumptions -> t > 0 && a > 0 && b > 0]
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| May 14, 2022 at 14:25 | history | edited | user14634 | CC BY-SA 4.0 |
added 83 characters in body
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| May 14, 2022 at 14:19 | history | asked | user14634 | CC BY-SA 4.0 |