You will need to know something about what you are integrating. Is it a periodic function? If so, you can convert that to an integral over just one period. If not, does your function taper off to zero at it approaches +/- infinity? If so, choose your limits by looking for convergence. That is, keep making them bigger until your answer changes less than some acceptable threshold. If your function does not taper off to zero, I am not sure what you can do. Perhaps you can use the symbolic toolbox in this case.

For symbolic algebra, I would recommend (further to paper and pencil) Maxima (wxMAxima).

It helped me substantially when dealing with exact those integrals you mean, requiring gamma (complete and incomplete) functions.

Open source too! BTW, I compiled a list of open source software for science and engineering. For symbolic tools, check under the heading "Scientific Programming" here:

http://emlab.utep.edu/resources.htm

Thanks for answers. what is the significance of gamma function and incomplete gamma function why they appear as a product with some other function in many solutions to some integrals. provide some link for understanding please.for computation we need to have solutions of these like definite intergals through putting some argument value ,are they called for solutions or they must require

well the Gamma function is the Generalisation of the factorial function Extended for non integer arguments.