Question: differentiating an integral w.r.t. a parameter

I woud like to have some help in using Maple to solve some complicated integrals.Specificaly, I would like to take the help of maple in differentiating an integral w.r.t. a parameter.

First, I will start with an integral for which Maple gives a solution. Let me first start with the assumptions :

Then, I will define my first function

If we integrate,

we get

Is there any way of completely removing the assumption sign for the parameters a and b? I don't need any reminders that I am asuming values (correct for my physical problem).

Now, I will define my next function

Integrating this function, we get

Maple does not give a solution.

I have, on my own, shown that the solution is :

I would like know how I can program Maple to get the same solution.

The first step in obtaining a soution is to differentiate the integral I2 with respect to b.

I would ike to show that the solution ies in ing the differential equation (the integral I2 is denoted as I) :

I am new to Maple. Can I get some help here? Actually, I am interested in solving more complicated integrals. When I know how I can program in Maple, I can move on to these more complicated integrals.

When I first tried the integration w.r.t. the parameter b (with the assumptions), I could not get the solution shown above. Should I take away the assumptions (which is only logical when differentiang wrt it). Actually, I got the solution above only after I started formulating this question for this newsgroup. The reason why I started with the assumption is that I did not want any compex solutions (which I got for another problem). So, the question is really if it is possibe to relax the assumptions just for the sake of differentiating the integral.

On a side note, when verifying the solutions, I could not succeed in using evalf with pi. For example,

does not give a numerical value.

Is there some way of forcing Maple to return a numerical value with a desired precision?


I will appreciate any help that I can get.



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