I would be very grateful if someone could help me with finding the integral for this little fellow...
1/ (x*((1-x)^0.5))
I have tried the few integration methods I know of (I've just finished A-Level), such as substitution and by parts, but they didn't appear to work. In addition, I put this into Wolfram's online integrator, and it came up with answer in a form I didn't understand, something to do with hypergeometric functions. I tried reading the article on them, but I couldn't see how to apply it to this problem. Are hypergeometric functions necessary for tackling this problem? They certainly look very confusing...
Thank you in advance!!
Jessica.
It's a standard solution but if you've got to show steps, you can do this. I've done this question and it's got a few steps so I'll explain instead of showing all steps. You can use substitution but not just one, it requires multiple substitution.
Substituting and doing the sorting out will lead to...
Here, substituting and doing the sorting out will lead to...
Now, just split into partial fraction and integrate. (You may require one more substitution when integrating a fraction).
Remember to substitute all variables ( )to get the final answer in terms of . The answer will be