What is the Easiest Way to Solve an Integration Problem Involving Tan(x)?

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Homework Help Overview

The discussion revolves around solving an indefinite integral involving the tangent function, specifically focusing on integration techniques and substitutions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of u-substitution and the derivative of the tangent function as a starting point for the integral. Some express uncertainty about their understanding and seek clarification on the substitution process.

Discussion Status

The conversation includes attempts to clarify the integration process, with some participants suggesting alternative substitutions. There is acknowledgment of previous misunderstandings, but no explicit consensus on the best approach has been reached.

Contextual Notes

Participants mention the need to simplify the integral and consider constants in their substitutions, indicating a focus on the nuances of integration techniques.

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Solved. Thanks.
 
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The simplest way to solve that indefinite integral is to realize that

\frac{d}{dx}tan x = sec^{2}x , and try a u-substitution from there...
 
meiso said:
The simplest way to solve that indefinite integral is to realize that

\frac{d}{dx}tan x = sec^{2}x , and try a u-substitution from there...

Yes, sorry, i am stupid. I realized that 2 minutes after posting here. I'm pretty sure i have it now. It's just -(2+u)^{-1} for u=tanx, right? And thanks for the reply.
 
Noo said:
It's just -(2+u)^{-1} for u=tanx, right? And thanks for the reply.

No problem. And, actually, you can set u = tan(x) + 2 to make things even easier. 2 is just a constant, so the derivative of tan(x) is the same as the derivative of tan(x) + 2.
 

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