HELPPP, Integral of Tan^3(PI times X)dx

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Homework Help Overview

The discussion revolves around the integral of Tan^3(πX) with respect to X, exploring various approaches to tackle the problem within the context of calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to manipulate the integral using trigonometric identities and considers a substitution method. Some participants suggest splitting the integral into two parts and using different substitutions for each part, while others express uncertainty about the next steps.

Discussion Status

The discussion is active, with participants offering different strategies and acknowledging each other's contributions. There is a sense of collaborative exploration, but no consensus has been reached on a definitive method or solution.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available for the problem. There is also a mention of using approximations for π, which could influence the setup of the integral.

Arjun571
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Homework Statement


Integral of Tan^3(PiX)dx


Homework Equations





The Attempt at a Solution


Int= Integral
PI=22/7
Int Tan^3(22/7X)dx
=Int Tan(22/7X)Tan^2(22/7X)dx
=Int (Sec^2(22/7X)-1)(Tan(22/7X)dx
=Int (Tan(22/7X)Sec^2(22/7X)-Tan(22/7X)dx
=...?
Im lost as to where to go from here, should i use a U substitution for one of them?
 
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Split the integral as two integrals now.

so you have

∫tan(πx) sec2(πx) dx - ∫ tan(πx) dx

for the first integral, you can use u=tan(πx) and for the second one, rewrite tan as sin/cos.
 
oooh, i don't know how i didnt seen that before, thanks a lot man
 
[tex]I = \int \tan^3 x \, dx = - \int d\cos x \, \frac{1-\cos^2 x}{\cos^3 x} = ...[/tex]
 

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