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Integral of x sqrt( x/(x-1))

  • Thread starter Sidthewall
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  • #1
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Homework Statement


integral of x *sqrt( x/(x-1))


Homework Equations





The Attempt at a Solution


I honestly don't know how to approach this i dont see any type of trig substituions whatsover, I really need some kind of lead and an explnation y that method works
 

Answers and Replies

  • #2
gabbagabbahey
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Homework Statement


integral of x *sqrt( x/(x-1))


Homework Equations





The Attempt at a Solution


I honestly don't know how to approach this i dont see any type of trig substituions whatsover, I really need some kind of lead and an explnation y that method works
Hmmm... I guess I'd start by making the substitution [itex]u=\frac{x}{x-1}=1+\frac{1}{x-1}[/itex] in order to get rid of the junk inside the square root. You'll probably find that doing this will allow you to split the integral into two easier integrals since [itex]x=1+\frac{1}{u-1}[/itex]
 
  • #3
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Homework Statement


integral of x *sqrt( x/(x-1))


Homework Equations





The Attempt at a Solution


I honestly don't know how to approach this i dont see any type of trig substituions whatsover, I really need some kind of lead and an explnation y that method works
I haven't carried this all the way through, but I think it will work
[tex]\int x \sqrt{\frac{x}{x - 1}}dx = \int \frac{x^{3/2}}{\sqrt{x - 1}}dx[/tex]

I believe that an ordinary substitution will work.
Let u = sqrt(x - 1).
 
  • #5
vela
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You can integrate secn θ using integration by parts, letting u=secn-2 θ and dv=sec2 θ dθ. For sec5 θ, you'll have to do it twice. It's a bit tedious but straightforward.
 
  • #6
gabbagabbahey
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You don't actually need a trig sub. You can also use Partial Fraction Decomposition if you find that easier.
 

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