Maple cannot solve this integral

Posted on 2008-11-26 10:49 By areslagae (1)

Categories:

How do I ...? with Maple

Hello,

I am new to Maple. I am trying to solve a big integral, but I cannot solve it using Maple.

The problem boils down to this integral:

int(exp(x*cos(theta)+y*sin(theta)), theta=0..2*Pi)

The solution of this integral is:

2*Pi*BesselI(0, sqrt(x*x+y*y))

How can I get Maple to solve these integrals?

Bessel integrals

Comment on 2008-11-26 11:56 from Robert Israel ( Maple Rating 4

1555)

Maple does have trouble with integrals such as this. See e.g. www.mapleprimes.com/forum/integratingcossintheta.

Table integrals

Comment on 2008-12-01 01:30 from alec ( Maple Rating 4

1608)

That's strange. At least int(exp(z cos(t)),t=0..2*Pi) should be in the table of known integrals (if such a table exists). Then original integral could be calculated using transformation x cos(t) + y sin(t) = z cos(t-a) with z=sqrt(x^2+y^2), assuming that x and y are real, and noticing that it is an integral over a period allows to get rid of a.

Besides, it can be integrated by expanding exp as power series and integrating the series terms.

Alec

table of known integrals

Comment on 2008-12-06 01:19 from jakubi ( Maple Rating 4

943)

At least in the table `int/definite/table` it is not included (none of the integrals here is parametric). And it is neither in the table IntegrationTools:-Definite:-Integrators:-LookUp:-Algebraic:-Table