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

[intenzxboi]

Homework Statement

$$\int$$(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

 

[arildno]

Set u=e^-2x instead.
Therefore, du/dx=-2u, that is dx=-du/2u

Use this to simplify your integrand!

 

[intenzxboi]

k using u=e^-2x
du=-2 (e^-2x) dx

so...

-1/2 $$\int$$ sin u du

-1/2 (-cos u) + c is that right?

 

[Dick]

Sure. But there is a simpler way to write (-1/2)*(-cos(u)).

 

[intenzxboi]

so final answer is cos u /2

 

[Dick]

cos(u)/2+C. Use more parentheses. cos u /2 can also be read cos(u/2).