@pasmith I tried another approach obtaining the following, I do not know if it is correct
\begin{array}{l}\int_{ }^{ }\frac{1}{\sqrt{x^3+1}}dx\\
\int_{ }^{ }\left(x^3+1\right)^{-\frac{1}{2}}dx\\
\left(1+u\right)^R\ \ \left[u=x^3,\ R=-\frac{1}{2}\right]\\
f\left(u\right)=\left(1+u\right)^R\\...
what I did was the following, even though I am sure this is incorrect.
## I=\frac{1}{\sqrt{1+x^a}} ##
## \frac{dI}{dx}=-\frac{ax^{a-1}}{2\left(1+x^a\right)^{\frac{3}{2}}},\ \ \frac{d^2I}{dx^2}=-\frac{ax^{a-2}\left(-ax^a-2x^a+2a-2\right)}{4\left(x^a+1\right)^{\frac{5}{2}}} ##
##...
How do I obtain p (x) and q (x) ?, I had done similar exercises but in that case I did it from the solution already given ...
oh i got to solve the edo
## \frac{d^2I}{dx^2}+\frac{dI}{dx}+I=0 ##
and then replace?
I also don't understand how to get the descending factorials for this hypergeometric series, I also know that there is another way to write it with gamma functions, but in any case how am I supposed to do this?
If I write it as a general term, wolfram will give me the result
which leaves me...
damn I suck at this lmao
I think it's better if I just give up and that's it.
Do you have any video on yt that you can share with me to illustrate what you mean?
aaa already understand.
you mean the formula ## h / 4 ##?
If I replace values I do not get the same result so I assume that I am missing some concept
If you solve the integral in the form of its symbols, I will obtain the "formula" for this case, right?
Hmm, the problem tells us to locate the centroid of the area shaded in blue in Z, and according to the figure that is a known data from 0 to 2, right?
There are several formulas, so I would not know which one to apply here.
ummm I don't understand what you mean by this, could you give me another example?
I saw that there were several formulas depending on the case, but I doubt that my professor would like me to use them.