hgd7833 Posted April 14, 2012 Share Posted April 14, 2012 How to find the imporper integral from - 00 to 00 of f(x) = (e^(ikx)).(1-e^x / 1+e^x) where k is a real fixed number ?? I tried to write e^ikx = coskx + i sinkx but i don't know what to do with the term multiplied by e^ikx which is (1-e^x / 1+e^x) ?? Thank you Link to comment Share on other sites More sharing options...
Anvar Posted April 14, 2012 Share Posted April 14, 2012 How to find the imporper integral from - 00 to 00 of f(x) = (e^(ikx)).(1-e^x / 1+e^x) where k is a real fixed number ?? I tried to write e^ikx = coskx + i sinkx but i don't know what to do with the term multiplied by e^ikx which is (1-e^x / 1+e^x) ?? Thank you Are you shure the integral is findable? Link to comment Share on other sites More sharing options...
hgd7833 Posted April 14, 2012 Author Share Posted April 14, 2012 Yes , that's what the professor said. Link to comment Share on other sites More sharing options...
hgd7833 Posted April 15, 2012 Author Share Posted April 15, 2012 Isn't correct that i-e^x / 1+e^x = - tanh(x/2) ??? If yes, then how can we proceed ?? Link to comment Share on other sites More sharing options...
QuantumBullet Posted December 18, 2012 Share Posted December 18, 2012 It may be easier to work with if you first rearrange the fraction: (1-e^x / 1+e^x) = 1 - (2e^x / 1+e^x). Since the integral of this latter fraction is more easily calculable, and is equal to x - 2ln(1+e^x) Link to comment Share on other sites More sharing options...
caKus Posted December 21, 2012 Share Posted December 21, 2012 I submitted it to WolframAlpha http://www.wolframalpha.com/input/?i=improper+integral+calculator for k = 0 and 1. It could find an antiderivative, but the integral diverges. Perhaps hdg7833 have been given the solution by his professor, now, and he can share it with us ? Link to comment Share on other sites More sharing options...
stardustbrain Posted January 7, 2013 Share Posted January 7, 2013 How to find the imporper integral from - 00 to 00 of f(x) = (e^(ikx)).(1-e^x / 1+e^x) where k is a real fixed number ?? I tried to write e^ikx = coskx + i sinkx but i don't know what to do with the term multiplied by e^ikx which is (1-e^x / 1+e^x) ?? Thank you I'm confused. Is there something I'm missing? Is that a limited of integration? Link to comment Share on other sites More sharing options...
x(x-y) Posted January 11, 2013 Share Posted January 11, 2013 (edited) I obtain this solution as an indefinite integral: [latex]e^{\frac{ik}{2}}\left(2e^{\frac{1}{2}}-1\right)u + 2\left(1-e^{\frac{1}{2}}\right)ln|u| + C[/latex] Edited January 11, 2013 by x(x-y) Link to comment Share on other sites More sharing options...
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