I tried writing this as a 1/2 power and making a u substitution of the bracket. But then what do you do with the dx? I mean you have an integration of u wrt x? I forget how to do this?
These two both quadratics but I forget when to use parfrac or when to try completing the square. I can't decide how to start these? Please somebody help, thanks.
Look at this tool.
Be sure to click Show Steps
This is above and beyond the level expected on this course... there must be a simpler way?
How would you KNOW when to use what substitution, please?
I arrive at What are they (Wolfram) doing with the first term?
My main concern, however, is how you know to use the substitution
Also, how about the other q's?
Plato, thanks for the link, yes, I can follow every step. The only things I don't get are:
Knowing that you have to make this substitution (I understand with hindsight, but how to know beforehand)
What they are doing with the sin(2arcsin(x/2)) to put it back in to a root?
Why do it? Because its in the paper...
For the second question, I got Stephen makes it slightly different with instead of and I'm wondering if this matters at all? (Since technically its modulus of the log its the same thing). It also uses a completely different method (I used parfrac) but I think I have the same result?