How Can I Integrate x*sqrt(1-x^4) Using Trig Substitution?

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Discussion Overview

The discussion revolves around the integration of the expression x*sqrt(1-x^4) using trigonometric substitution. Participants explore different substitution methods and seek clarification on the integration process.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to begin the integration of x*sqrt(1-x^4).
  • Another participant proposes a substitution of u = x^2, leading to a transformed integral involving sqrt(1-u^2).
  • A later reply suggests using the substitution u = sin(w) for the integral, indicating a potential direction for solving it.
  • Participants confirm the appropriateness of the suggested substitution and express readiness to proceed with the integration.

Areas of Agreement / Disagreement

Participants generally agree on the substitution method proposed, but the overall integration process remains unresolved.

annie122
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how do i go about integrating

x*sqrt(1-x^4)??

i have no idea
 
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Re: another trig substitution

Yuuki said:
how do i go about integrating

$$\int x \cdot \sqrt{1-x^4}dx$$

i have no idea

I would let $$u = x^2 \therefore du = 2x dx$$

$$\int x \cdot \sqrt{1-x^4} \cdot \dfrac{du}{2x} = \dfrac{1}{2} \int \sqrt{1-u^2} du$$

Do you know a trig sub for this integral?
 
Re: another trig substitution

u = sin(w) right?

thx!
 
Re: another trig substitution

Yuuki said:
u = sin(w) right?

thx!

Yes, that's the right sub to use. Are you ok going forward?
 
yup thank you
 

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