Integrate (e^2t+e^-2t+2)^(1/2) w.r.t t - Step by Step Guide

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Homework Help Overview

The original poster attempts to integrate the expression (e^2t + e^-2t + 2)^(1/2) with respect to t. The subject area involves calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Some participants suggest transforming the expression into a perfect square as a potential approach. Others mention integration by parts as an initial attempt. There is also a discussion about finding the inverse of a related expression and the challenges faced with logarithmic manipulation.

Discussion Status

The discussion is ongoing, with participants exploring different methods and transformations. Some guidance has been offered regarding manipulating the expression into a quadratic form, but there is no explicit consensus on a complete solution.

Contextual Notes

Participants are navigating through various integration techniques and transformations, with some expressing uncertainty about the effectiveness of their approaches. There are indications of related problems being discussed, which may influence the current problem's context.

akoska
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For part of a problem, how would I integrate:

(e^2t+e^-2t+2)^(1/2) with respect to t

I have no idea..., but I've tried integration by parts to start...
 
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can you transform e^2t+e^-2t+2 into a perfect square?
 
Ok, i see now. Thanks.

I have another problem now... I found the solution to be a=exp(t)-exp(-t) and I need to find the inverse of a. Taking the ln of each side didn't help at all.
 
Last edited:
multiply by exp(t) and bam you got a quadratic!
 

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