Integration using Euler's formula: Difference between revisions

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Alternatively, we may also take note of real and imaginary portions of complex numbers
 
Cosine is the real portion of a complex number written in cos  ''x '' +  ''i '' sin  ''x'' form.
 
: <math>\int e^x \cos x \, dx</math>
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: <math>\int e^x \mathrm{Re}\{ e^{ix} \} \, dx</math>
 
: <math>\mathrm{Re}\left\{ \int e^x e^{ix} \, dx \right\}</math>
 
: <math>\mathrm{Re}\left\{ \int e^{(i+1)x} \, dx \right\}</math>