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anonymous
 5 years ago
need help with evaluating this integral.... (x^9)/(sqrt(3+x^5)) dx.....
anonymous
 5 years ago
need help with evaluating this integral.... (x^9)/(sqrt(3+x^5)) dx.....

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I would recommend a u substitution of u = x^5+3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i started that....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then i got (1/5)du = x^4dx ....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, though I prefer dx = du/(5x^4)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So then, what is x^5 in terms of u?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i dont know what you mean by that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0u = x^5 + 3 so x^5 = ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok. Good. Now start substituting in your integral

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so whats the x^9?... the denominator will be sqrt3?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The denominator will be \(\sqrt{u}\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats what i meant.///

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the dx will be \[\frac{1}{5x^4}du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So what's left in the numerator( after you simplify)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Cmon. \[\int \frac{x^9}{\sqrt{x^5+3}}dx = \int \frac{x^5 * x^4}{\sqrt{x^5+3}}dx \] \[\text{Let }u = x^5+3 \]\[\implies x^5 = u3 \] \[\implies 5x^4dx = du \implies dx = \frac{1}{5x^4}du\] Therefore \[\int \frac{x^5 * x^4}{\sqrt{x^5+3}}dx = \int \frac{(u3)*x^4}{\sqrt{u}} (\frac{1}{5x^4})du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And we can cancel the x^4 from top and bottom. Then split the fraction into two different fractions \[\frac{u}{\sqrt{u}}  \frac{3}{\sqrt{u}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and integrate each one separately.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what happened to the 5 in the faraction

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes there should be a factor of 5 outside the integral , he most likely didnt mention it because any integral of a constant multiple is just the integral times that constant
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