Loser66
  • Loser66
\(\int \dfrac{sin^2x}{7e^x}dx\) Please, help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Loser66
  • Loser66
@zepdrix
ganeshie8
  • ganeshie8
use the identity \(\sin^2x = \frac{1-\cos (2x)}{2}\), the integral becomes \[\frac{1}{14}\int e^{-x}\, dx-\frac{1}{14}\int e^{-x}\cos(2x)\, dx\]
Loser66
  • Loser66
Yes, I did

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ganeshie8
  • ganeshie8
There are several ways to evaluate an integral of form \(\int e^{ax}\cos(bx)\, dx\) there is really a very neat method if you're okay with complex numbers
Loser66
  • Loser66
ah, you want to express it in term of Euler?
Loser66
  • Loser66
I am ok with any method, please. show me. I can't get the answer as what wolfram does.
Loser66
  • Loser66
ok, go ahead, please
ganeshie8
  • ganeshie8
Yes : \[\large e^{-x}\cos(2x) = \mathcal{R} (e^{-x+i2x})\]
ganeshie8
  • ganeshie8
we're done, integrating \(e^{-x+i2x}\) is a piece of cake
ganeshie8
  • ganeshie8
\[\begin{align} \int e^{-x}\cos(2x) \,dx &= \mathcal{R} \int e^{-x+i2x}\,dx\\~\\ &= \mathcal{R}~ \dfrac{e^{-x+i2x}}{-1+2i}\\~\\ \end{align}\] just get the real part of that expression and yeah don't forget the integration constant..
Loser66
  • Loser66
Got you, thank you. Much appreciate. :)
ganeshie8
  • ganeshie8
np :)

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