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Edited by KommaH, Andrew Slattery, Maluniu

Integration by parts is an essential method of integration that any student should know while taking mid to upper-level Calculus classes. Integrals involving multiplication that would otherwise be difficult to solve can be easily put into a simpler form using this method of integration.

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Steps

  1. Integration by Parts Step1.png
    1
    Determine whether or not integration by parts should be used on the integral given. Remember that integration by parts works best on integrals that appear to have two parts that are being multiplied. If there is any addition involved in the integral, chances are that you shouldn't be using integration by parts,
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  2. Integration by Parts Step2.png
    2
    Recall the formula for integration by parts. The formula for integrating by parts is ∫u*dv = u*v - ∫v*du. You will need to find all the components for the formula before you can actually solve the integral.
  3. Integrate by Parts Step3.png
    3
    Select the part of the equation to be integrated to be u. The rest of the equation should be selected as dv. When choosing u, choose the side of the equation that you think will be the easiest to differentiate.
    • For this part, it helps to use a table or a chart to keep track of u, du, v, and dv.
  4. Integrate by Parts Step4.png
    4
    Solve for du and v. In order to solve for du, simply differentiate u. To solve to v, integrate dv. In this example, du could also be written as 1*dx. Don't be confused by the notation. 1*dx is simply just dx.
  5. Integrate by Parts Step5.png
    5
    Now that you have u, du, v, and dv, put the integral in the form of ∫u*dv = u*v - ∫v*du. Note that you still have one more integral to solve for.
  6. Integrate by Parts Step6.png
    6
    Integrate ∫v*du.
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Tips

  • Don't forget to add + C if evaluating an indefinite integral!
  • If trying to differentiate u is too hard or if trying to integrate dv is too hard, try switching dv and u.
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Related wikiHows

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How to
Integrate by Substitution

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Integrate by Parts when One Function Is a Polynomial

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Recent edits by: Andrew Slattery, KommaH

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