Integrating nested root in denominator

[fintian]

Hi Y'all,

I was trying to integrate a function in two dimesions. after integrating it in one dimesion and substituting the limits I got two terms.

I am unable to integrate the second term. That is because it had a sqare root in the denominator which contained another one within it. I took out unnecessary parameters and simplified this term to present it here.

now ____________________________________1
The function to be integrated: -------------------------------
_____________________________________________2 2
__________________________Sqrt[a + c x + b Sqrt[r - x ]]

this is equivalent to = 1/(a+b*(r^2-x^2)^(1/2)+c*x)^(1/2)

I tried using mathemetica but it just gives the input as output with an integratin symbol on it.

Can someone please help!

thanks for reading! many more thanks if you can solve!

 

[Integral]

The equations you need to show us are very hard to read in text fromat read this thread for a better way.

 

[M98Ranger]

Hi there,

Integrating nested roots in the denominator can be tricky, but there are a few approaches you can try. One option is to use a substitution to simplify the nested root. For example, you could let u = sqrt(r-x^2), which would turn the denominator into (a + b*u + c*x)^(1/2). This may make the integration easier, as you can now treat u as a constant and integrate with respect to x.

Another approach is to use partial fractions to break up the fraction into simpler terms. This can be helpful when dealing with nested roots, as it allows you to separate the terms and integrate them separately.

I would also suggest checking your limits of integration to make sure they are appropriate for the function you are integrating. Sometimes, a change of variables can help with this as well.

I hope this helps. Good luck with your integration!