Okay, I generally have no problems, except when the derivative of the term that needs to be substituted is a constant, say, 1 and the coefficient of the or whatever in the original question is a pronumeral, say, .
Here is an example:
Find the integral between and where using the substitution
I have found that, by differentiation,
My problem is:
Once i get to this stage:
and the then becomes
but what about the ?
how do I get that into ?
if the differentiated had an in it, then fine, I could do that, but since it doesn't, I'm in a pickle.
And you can only have constant terms in front of the whole integral such as
But what do I do for these types of integrals?