How to handle leftover terms in integration after substitution?

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Homework Help Overview

The discussion revolves around the integration of the function \(\int \sec^3 x \tan x \, dx\). The original poster is exploring substitution methods, specifically using \(u = \tan x\) and \(du = \sec^2 x \, dx\), and is encountering difficulties with a leftover \(\sec x\) term after substitution.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss different substitution methods, including the suggestion to use \(u = \sec x\). There is a focus on how to handle the remaining \(\sec x\) term after substitution. The original poster expresses confusion about the latex formatting as well.

Discussion Status

Some participants have offered alternative substitution suggestions, and there appears to be a productive exchange of ideas. The original poster acknowledges receiving helpful input, indicating some progress in understanding the integration process.

Contextual Notes

The original poster mentions being new to latex, which may affect their ability to communicate mathematical expressions clearly. There are also requests for resources on using latex effectively.

Triggy
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How do you integrate [tex]\int secx^{3}tanxdx[/tex]

I'm substituting [tex]u = tanx[/tex] so [tex]du = sec^2xdx[/tex]Now the problem is when I made sec^3x into sec^2xsecx then I had a secx left over after my substitution. What do I do with this?

PS: Sorry I'm new at latex and I don't know how to get rid of that {
 
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Try sec(x) = u and substituting. When you differentiate this it may become clearer.
 
Aahh! Thanks tending to infinity man. I got it.

[tex]\{1/3sec^3x} [\tex][/tex]
 
Is there like a post on how to use latex?
 
Triggy said:
Is there like a post on how to use latex?

If you click on latex images it shows you the code and there is a link below the code to a short PDF with a few tips and small tutorial.

https://www.physicsforums.com/misc/howtolatex.pdf
 
Triggy said:
PS: Sorry I'm new at latex and I don't know how to get rid of that {

Delete the \{ and the }.
 
Awsome. Thanks Kurdt and GJ
 

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