Why Is Substitution Failing in Integrating This Function?

songoku
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Homework Statement
Find
$$\int \frac{x^3}{\sqrt{16x-x^8}}dx$$
Relevant Equations
u - substitution

trigonometry substitution
I tried using substitution ##u=\sqrt{16x-x^8}##, didn't work

Tried factorize ##x## from the denominator and then used ##u=\sqrt{16-x^7}##, didn't work

Tried using ##u=x^4## also didn't work

How to approach this question? Thanks
 
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songoku said:
Tried factorize ##x## from the denominator and then used ##u=\sqrt{16-x^7}##, didn't work
This was the right approach, but your u-sub is too fancy. Use a different u-sub from the expression ##\sqrt{x(16-x^7)}##.
It falls into place after that. In this problem you'll have to bring something back from outside the square root (which you'll see once you use the right U-sub), a complete the square, and a trig sub.
 
Thank you very much for the help romsofia
 
##u=\frac{x^{7/2}}{4}## looks promising
 
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