First some integrals with powers:

Here we have several typical trigonometric integrals:

Some basic hyperbolic integrals:

And finally some integrals with quadratic expression (always A > 0):

More extensive lists of integrals contain hundreds of solved integrals, often very general, so if you have them available, it will simplify your life a lot. In such lists you may find for instance the following integrals: