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

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To integrate x*sqrt(1-x^4), the suggested substitution is u = x^2, leading to du = 2x dx. This transforms the integral into (1/2)∫sqrt(1-u^2) du. A further trigonometric substitution of u = sin(w) is recommended for simplification. The discussion confirms the validity of this approach and expresses readiness to proceed with the integration.
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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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