anonymous
  • anonymous
Integration
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\int\limits_{?}^{?} \frac{ 1 }{ \sqrt{x}(1+x) }\]
anonymous
  • anonymous
The question marks are not suppose to be there, so it's the problem without the question marks.
experimentX
  • experimentX
\int just use like this for integration ... seems like trig subs seems to work also changing 1 + x = (1 + i sqrt(x))(1 - i sqrt(x)) and then taking partial fraction might work.

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More answers

anonymous
  • anonymous
i believe u-sub will work
anonymous
  • anonymous
\[u=\sqrt{x}\] ha?
experimentX
  • experimentX
woops!! that also works!!
anonymous
  • anonymous
For this exercise, I'm technically not suposed to use partial fractions
anonymous
  • anonymous
I may be missing something, but I can't seem to find the answer with u = \[\sqrt{x} \]
experimentX
  • experimentX
change all x's into u's probably you would end up with 1/1+u^2 or something like that.
zepdrix
  • zepdrix
You have to mess with the U a little bit kore :) but it will work.
hartnn
  • hartnn
x= tan^2 theta might work
experimentX
  • experimentX
this is same as using trig subs x = tan^2 theta in original.
experimentX
  • experimentX
but lol ... we know int 1/1+x^2 = arctan (x) which is one of the standard integral.
anonymous
  • anonymous
I got it! Yes!!! I was substituting the first \[\sqrt{x} \] in the integrand. Then, I realized that it gets canceled out. Thank you very much everyone! ... If it wasn't for you, I probably would have spent another 10 minutes on this. -.-

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