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tsghernanBest ResponseYou've already chosen the best response.0
\[\int\limits_{1}^{9} \frac{ 1 }{ \sqrt{x*\sqrt{1+\sqrt{x}}} } \delta x \] (The integral is between 9 and 1
 one year ago

g152xxBest ResponseYou've already chosen the best response.0
@TuringTest is here so have no fear ! :)
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
Why do some people think I am a math demigod? I have no idea.... at least not yet.
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
try rewriting this with fractional powers instead of nested sqrts
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
then do a usubstitution where u = sqrt(x) (i'm just eyeballing this but it seems like this should work)
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
you ought to try some of the things you suggest or it just becomes a flood of ideas rather than an clear approach that will help the asker.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
No, substitute u = 1 + x^(1/2) Then du = (1/2)x^(1/2) dx and then easy to solve from that point.
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
heh, same thing, just off by 1 (du is still the same)
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
@tcarroll010 yes, I agree :)
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
@cnknd , it is necessary to isolate that term of "1" into u along with the x^(1/2)
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
i don't think it's all that difficult to integrate (1+u)^(1/4) rather than u^(1/4)
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
\[2\int\limits_{}^{}\frac{ du }{ \sqrt{u} }\]
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
\[= 4\sqrt{u}\]Now, just put the expression for u back in.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
\[4\sqrt{1 + \sqrt{x}}\]And you're done.
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
@tcarroll010 you forgot the a 2nd sqrt. it's \[2\int\limits_{2}^{4}\frac{ du }{ \sqrt{\sqrt{u}} }\]
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
Did not forget. Go back and look at the du equation. sqrt(x) is already in it.
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
original eqn had 3 sqrts
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
They get resolved in the du equation. Simply take the derivative of my answer and you'll see.
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
the first sqrt from the original expression covers both the x and the sqrt(1+sqrt(x)) unless my eyes are deceiving me.
 one year ago

g152xxBest ResponseYou've already chosen the best response.0
@cnknd  @tcarroll010 is right, take a look again.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
Simply rewrite the original equation to\[\frac{ 1 }{ \sqrt{x}\sqrt{1 + \sqrt{x}} }\]and then it will be clearer. Again, just take the derivative of my answer and you'll get the original equation, written either way.
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
original integrand was: \[\frac{ 1 }{ \sqrt{x \sqrt{1+\sqrt{x}}} }\]
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
yes, which is the same as my rewrite.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
@cnknd  @tcarroll010 is right  he is making use of this:\[u = 1 + x^{1/2}\]Then\[du = (1/2)x^{1/2} dx=\frac{dx}{2\sqrt{x}}\]
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
let \[A = \sqrt{1+\sqrt{x}}\] the original integrand would be: \[\frac{ 1 }{ \sqrt{xA} }\] and your rewrite is: \[\frac{ 1 }{ \sqrt{x}*A }\] im pretty sure those are different
 one year ago

tsghernanBest ResponseYou've already chosen the best response.0
I can solve it. Thank you guys
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
if you want to double check your answer, here's wolframalpha's solution: http://www.wolframalpha.com/input/?i=integrate+%281%2Fsqrt%28x*sqrt%281%2Bsqrt%28x%29%29%29%29
 one year ago

tsghernanBest ResponseYou've already chosen the best response.0
tcarroll010 was right. The best way is substitute u = 1 + x^(1/2)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
oh  sorry @cnknd  I thought you were wondering where the \(\sqrt{x}\) went. you are right  there should be an extra sqrt there.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
@tsghernan  please take note of what @cnknd was saying as well  there is an extra sqrt to put in
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
thank you sir moderator :) and yea u = 1 + x^(1/2) is easier than what i suggested
 one year ago

tsghernanBest ResponseYou've already chosen the best response.0
Yes. I know it. I verified the result with the mathematica soft. I reached it. Thank you a lot
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
I do believe @cnknd has a point. It looks like \[2\int\limits_{}^{}\frac{ du }{ \sqrt[4]{u} }\]is the integral to be considered. How does that look to you now, @cnknd?
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
yea that's what i meant.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
and then (8/3)u^(3/4) with the eventual substitution of u in terms of x. Is that what you are getting?
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
Good catch @cnknd !
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.4
So, the answer is derived with a combination of my substitution equation of u = 1 + x^(1/2) (to resolve the other x^(1/2), that part is correct ) and @cnknd 's correction on the exponent on u going from 1/2 to 1/4.
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
nice to see a "team" working towards a solution :)
 one year ago
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