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anonymous
 one year ago
integral (cos x)e^x using euler's formula
anonymous
 one year ago
integral (cos x)e^x using euler's formula

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.3What is the Euler's formula?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cos=(e^ix+e^ix)/2 and sin (e^ixe^ix)/2i

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Confirm: What is your problem? \[\int cos(x) e^{x}dx\] or \[\int cos (x) e^{ix} dx\] Which one?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3I am doubt myself when I take it easy!! ha!! \[\int cos(x) e^{x}dx =\int \dfrac{e^{ix}+e^{ix}}{2}e^{x}dx\] =\[1/2\int e^{x(i1)}dx +1/2\int e^{x(i+1)}dx\] For the firs one, it is equal \(= \dfrac{1}{2}\dfrac{e^{x(i1)}}{i1}+C\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Do the same with the second one and simplify if it is needed. But I am not confident on it since it is quite easy like that.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2\[ (cos x)e^{x} = \mathcal {Re} \ e^{ix} \ e^{x}\] \[\ \implies \mathcal{Re} \ \int \ e^{(1+i)x} \ dx \] \[= \mathcal{Re} \ \frac{1}{1+i} \ e^{(1+i)x}\] \[= \mathcal{Re} \ \frac{1i}{2} \ e^{x} \ e^{ix}\] \[= \ \frac{ e^{x}}{2} \mathcal{Re} \ (1i). (cos x + i sin x)\] \[= \ \frac{ e^{x}}{2} \mathcal{Re} (cosx + sin x + i[cosx sinx])\] \[=\frac{ e^{x}}{2} (cosx + sin x)\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2oooops! that is a complete solution which is a bad, bad thing  mea culpa, my bad  but you presumably know he answer anyway and are looking into some methods to do it and this is @Loser66's approach with a slant.
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