Integration by substitution for integral

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Homework Help Overview

The discussion revolves around evaluating the integral \(\int \frac{4\cos(t)}{(2+\sin(t))^2}dt\) using substitution methods. Participants are exploring the appropriate substitution to simplify the integral.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about the choice of substitution, having attempted various forms without success. One participant suggests using \(u=2+\sin(t)\) as a potential substitution.

Discussion Status

The discussion is ongoing, with participants sharing thoughts on substitution strategies. Some guidance has been provided regarding the use of simpler substitutions before considering more complex ones.

Contextual Notes

There are no specific equations provided for reference, and the original poster indicates a lack of clarity on the substitution process.

adartsesirhc
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Homework Statement


Use substitution to evaluate the integral.
\int \frac{4cos(t)}{(2+sin(t))^2}dt

Homework Equations


None, really.

The Attempt at a Solution


I'm not sure what to use as u, for the substitution. I've tried (2+sin(t))^2, as well as other attempts, but I can't seem to find anything.
 
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Sorry, I meant
\int \frac{4cos(t)}{(2+sin(t))^2}dt
 
Why not try u=2+sin(t) ?:wink:
 
adartsesirhc said:

Homework Statement


Use substitution to evaluate the integral.
\int \frac{4cos(t)}{(2+sin(t))^2}dt


Homework Equations


None, really.


The Attempt at a Solution


I'm not sure what to use as u, for the substitution. I've tried (2+sin(t))^2, as well as other attempts, but I can't seem to find anything.

Always try a simple substitution before you try the more complicated substitutions. If your simple substitution doesn't work, you won't have wasted much time.
 

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