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Mathematics LibreTexts

7.8: Homework- Integration by Parts

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  1. Solve each of the following using integration by parts:
    1. xcos(x)dx
      xsin(x)+cos(x)+C
      ans
    2. (4x1)cos(x)dx
      (4x1)sin(x)+4cos(x)+C
      ans
    3. xsin(x)dx.
      xcos(x)+sin(x)+C
      ans
    4. xexdx.
      xexex+C
      ans
    5. ln(x)dx. (Hint: Let u=ln(x) and v=1)
      xln(x)x
      ans
  2. Watch the following Khan Academy video: Integration by parts twice
  3. Use integration by parts to solve x2cos(x)dx.
    x2sin(x)+2xcos(x)2sin(x)+C
    ans
  4. Use integration by parts to solve x3exdx.
    x3ex3x2ex+6xex6ex+C
    ans
  5. Watch the following Khan Academy video: Integration by parts with e and cos together.
  6. Use integration by parts to find exsin(x)dx.
    sin(x)excos(x)ex2+C
    ans
  7. Two part question:
    1. Use u-substitution to find sin(2x)dx and cos(2x)dx.
      12cos(2x) and 12sin(2x)
      ans
    2. Use integration by parts to find xsin(2x)dx.
      12xcos(2x)14sin(2x)
      ans

This page titled 7.8: Homework- Integration by Parts is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Tyler Seacrest via source content that was edited to the style and standards of the LibreTexts platform.

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