I can see that
is easier to integrate, and can carry that integration out.
However, I can't see how your:
corresponds to
or how you got there.
This is as step by step as I can make it.
The original integral is
It's always a good idea to try to get the denominator to be as simple as possible. (Though there are exceptions to that.) So this gives the idea of the substitution
To sub this back into the integral we need to know what v is. So solving for v in terms of u we get:
But we are not done. We also need to find an expression for dv in terms of u also. So
Solving this for dv gives
Now we need to sub in our values for v and dv into the original integral:
Factoring out the constants gives
And subbing back in gives
-Dan
Topsquark, thanks again, I have, hopefully, one final question with regards to the above.
We have
yet, we have
I'm struggling with this, why does the derivative of v equal one third of the derivative of u (which of course would be 1)?
I think with a bit of clarification on this I will be done! I really appreciate your patience.