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

[annie122]

how do i go about integrating

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

i have no idea

 

[SuperSonic4]

Re: another trig substitution

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?

 

[annie122]

Re: another trig substitution

u = sin(w) right?

thx!

 

[SuperSonic4]

Re: another trig substitution

u = sin(w) right?

thx!

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

 

[annie122]

yup thank you