Integrating Trigonometric Functions: Secant and Tangent

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Homework Help Overview

The problem involves integrating a trigonometric function, specifically the integral of secant and tangent functions, expressed as ∫secxtan3x dx. The discussion centers around techniques for integration and manipulation of trigonometric identities.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss rearranging the integral and consider using substitution, with one suggesting that u could equal secx. There are attempts to express the integral in terms of secant and tangent functions, and questions arise about the validity of these transformations.

Discussion Status

The discussion includes various approaches to the integral, with some participants providing guidance on how to manipulate the integral using substitution. However, there is no explicit consensus on the final approach or solution, and the conversation remains open-ended.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information shared and the methods discussed. There is an emphasis on exploring different interpretations of the integral without arriving at a definitive conclusion.

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Homework Statement



∫secxtan3x dx

Homework Equations





The Attempt at a Solution


∫secxtanx(tan2x) dx
∫secxtanx(sec2x-1) dx

Is u supposed to equal secx?
 
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Du=Secxtanx
I like to rearrange my integral

∫(secx^2-1) secxtanx dx
------------(^ ^ Du^^)

Since you pulled out secxtanx as du.
and converted the remaining factors to secants.All you have to do now is
take the integral of
∫(secx^2-1) and that will be your answer
 

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Thanks
 
No problem! :)
 

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