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:

then and

then

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?