Can You Integrate x/sqrt(x(1-x))?

[peace-Econ]

sorry, is it possible to take integral from this: x/sqrt(x(1-x))

Need help! Thanks!

 

[stevenb]

sorry, is it possible to take integral from this: x/sqrt(x(1-x))

Need help! Thanks!

I believe it is possible. This is based on a quick look in an integral table.

 

[peace-Econ]

Thank you for replying, but sorry, what is integral table? could you show that...?

 

[stevenb]

Thank you for replying, but sorry, what is integral table? could you show that...?

You are welcome.

An integral table is just a listing of the integrals already worked our for you. Sometimes you can find your integral in a table and this tells you that it is possible to work out a solution on your own. Also, seeing the answer can help you figure out how to solve it. So, basically this is a time saver to make sure you don't waste your time down a hopeless path.

This is the old way. The youngsters like to use the various computer based symbolic processors (Mathematical, Maxima, Maple, Wolfram, etc.), but I'm kind of old fashioned. Still, if I don't find it in a table, I will try these good tools.

Anyway, I've attached a PDF of the page from my table and you can see that numbers 163 and 164 will give you the answer. If you are just trying to get the answer, then you are all set, however if you want to work out the method, you need to figure it out. Looking at the table, it's not hard to see how they figured this out. Number 164 can be found by adding a term that forces the integral to have a du/sqrt(u) form. Of course, if you add a term, then you have to subtract it also, and you get the additional integral. Number 163 gives you the clue to solve by making the appropriate substitution that will give the inverse sine solution.

 

[snipez90]

The typical way for dealing with this type of integral is to complete the square on the term inside the square root in the denominator. Once you do that, make the appropriate trig substitution and go from there.

 

[peace-Econ]

Thank you so much for your help!

 

[mrmiller1]

int(x/sqrt(x(1-x))) = 0.5(atan((x-0.5)/sqrt(-x(x-1))) - sqrt(x-x^2) + C