Educator

Integration Tables

Main formula:

Almost every calculus book has tables of integrals inside the back cover. You can also find tables on the web. To use these tables, you must make the integral you’re given match the pattern in the table exactly, including the du.

Hints and tips:

• For quadratic expressions, you often have to complete the square and make a substitution to make your integral match the one in the table.

• You also often have to make some other substitution like u = 3x. When you make these substitutions, make sure you convert the dx as well.

• Sometimes, the tables don’t give you full answers, but instead give you reduction formulas, such as how to reduce ∫ secⁿ x dx to ∫ secⁿ⁻² x dx. Then you may have to use the formulas more than once, or use the formula to reduce your integral to another integral that you will then solve directly.