Question

\(\int \dfrac{sin^2x}{7e^x}dx\)
Please, help

Answer 1

@zepdrix

Answer 2

use the identity \(\sin^2x = \frac{1-\cos (2x)}{2}\), the integral becomes

\[\frac{1}{14}\int e^{-x}\, dx-\frac{1}{14}\int e^{-x}\cos(2x)\, dx\]

Answer 3

Yes, I did

Answer 4

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

Answer 5

ah, you want to express it in term of Euler?

Answer 6

I am ok with any method, please. show me. I can't get the answer as what wolfram does.

Answer 7

ok, go ahead, please

Answer 8

Yes :
\[\large e^{-x}\cos(2x) = \mathcal{R} (e^{-x+i2x})\]

Answer 9

we're done, integrating \(e^{-x+i2x}\) is a piece of cake

Answer 10

\[\begin{align} \int e^{-x}\cos(2x) \,dx &= \mathcal{R} \int e^{-x+i2x}\,dx\\~\\
&= \mathcal{R}~ \dfrac{e^{-x+i2x}}{-1+2i}\\~\\
\end{align}\]

just get the real part of that expression and yeah don't forget the integration constant..

Answer 11

Got you, thank you. Much appreciate. :)

Answer 12

np :)