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Integration by Parts

Main formula:

Hints and tips:

• Integration by parts never solves the integral completely for you. The point is to reduce a difficult integral to an easier one.

• If you have a polynomial multiplied by an exponential or trigonometric function, you can use the tabular integration shortcut.

• You may have to use parts more than once in the same problem.

• Sometimes, after using parts one or more times, you get the original integral reappearing. Then you can set up an equation for the original integral and find the solution algebraically without doing any more integration.

• Use the mnemonic LIATE (Logarithmic, Inverse, Algebraic, Trigonometric, Exponential) to know which part of the expression to make the u.

• Sometimes you have to make one or more substitution before you get a form that works well for integration by parts.