How can I develop a computer program for indefinite integrals solution?

Answer 1

Well, if you want to save yourself a lot of work, you can start by modifying one that already exists. Look, for instance, at Maxima (http://maxima.sourceforge.net/ ), and its integrate function. It's open-source, so you can look at the inside of the program to get an idea of how it works.

Answer 2

Try Mathematica or some other symbolic-math software. Developing software would be difficult and it's already been done. It would require transforming integrands into standard forms and then looking them up in a table. Also, integrating by parts.