Ksoap2-android itself is licensed under an MIT license. It depends on other libraries licensed under different licenses.
Some source files include different licensing information in the header. In each case, they appear to be Apache and BSD licenses. If this is a concern, use care to examine the licenses and ensure they are compatible with your project.
It is the understanding of the current maintainers and committers that the licenses allow inclusion in proprietary application without a viral effect on the code of the application. We have not heard anything to the contrary from anyone, however we are not lawyers.
We would appreciate a credit in the application and a notification that you are using the library. It would also be great if you allow us to link to your application as a show case example.