Integrating sin(e^(-2x)) with Step-by-Step Solution

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Homework Help Overview

The problem involves integrating the function sin(e^(-2x)) divided by e^(2x), which falls under the subject area of calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss different substitutions for the integral, with one suggesting u = e^(-2x) and another proposing u = e^(2x). There is exploration of how to manipulate the integrand using these substitutions.

Discussion Status

The discussion is active, with participants providing alternative approaches and clarifying steps. There is a focus on simplifying the integrand and ensuring proper notation, but no consensus on the final expression has been reached.

Contextual Notes

Participants are navigating through the integration process and addressing notation issues, indicating a collaborative effort to clarify the solution without arriving at a definitive conclusion.

intenzxboi
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Homework Statement



[tex]\int[/tex](sin (e^(-2x))) / e^(2x)


The Attempt at a Solution



so i set
u=e^2x
du=(e^2x)(2) dx

im kinda stuck on how to get rid of the e^-2x
 
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Set u=e^-2x instead.
Therefore, du/dx=-2u, that is dx=-du/2u

Use this to simplify your integrand!
 
k using u=e^-2x
du=-2 (e^-2x) dx

so...

-1/2 [tex]\int[/tex] sin u du

-1/2 (-cos u) + c is that right?
 
Sure. But there is a simpler way to write (-1/2)*(-cos(u)).
 
so final answer is cos u /2
 
cos(u)/2+C. Use more parentheses. cos u /2 can also be read cos(u/2).
 

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