You'll find that there are many ways to solve an integration problem in calculus. The following list contains some handy points to remember when using different integration techniques:

  • Guess and Check. This technique works when the integrand is close to a simple backward derivative.

  • u-substitution. The integration counterpart to the chain rule; use this technique when the argument of the function you're integrating is more than a simple x.

  • Integration by Parts. Integration's counterpart to the product rule.

    1. Use this technique when the integrand contains a product of functions.

    2. Pick your u according to LIATE, box it, "7" it, finish it.

  • Trig Integrals

    1. Use Pythagorean identities.


    2. Use half-angle formulas.

  • Trigonometric Substitution. This method works when the integrand contains radicals of the forms


    (or powers of these roots), where a is a constant and u is an expression in x.

  • Partial Fractions. This technique works for rational functions (one polynomial over another).