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Another Trig Substitution

Yuuki

Member
Jun 7, 2013
43
how do i go about integrating

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

i have no idea
 

SuperSonic4

Well-known member
MHB Math Helper
Mar 1, 2012
249
Re: another trig substitution

how do i go about integrating

\(\displaystyle \int x \cdot \sqrt{1-x^4}dx\)

i have no idea
I would let \(\displaystyle u = x^2 \therefore du = 2x dx\)

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

Do you know a trig sub for this integral?
 

Yuuki

Member
Jun 7, 2013
43
Re: another trig substitution

u = sin(w) right?

thx!
 

SuperSonic4

Well-known member
MHB Math Helper
Mar 1, 2012
249
Re: another trig substitution

u = sin(w) right?

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

Yuuki

Member
Jun 7, 2013
43
yup thank you