How to Solve an Integration By Parts Problem?

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SUMMARY

The forum discussion centers on solving an integration by parts problem involving the equation (n-1)∫sin^(n-2)x(1-sin²x)dx. The user initially struggled with understanding step 6 of the solution but later identified their mistake as a misapplication of the Distributive Property. This highlights the importance of correctly applying algebraic properties in calculus problems, particularly in integration techniques.

PREREQUISITES
  • Understanding of integration by parts
  • Familiarity with trigonometric identities
  • Knowledge of the Distributive Property in algebra
  • Basic calculus concepts
NEXT STEPS
  • Review the principles of integration by parts
  • Study trigonometric identities and their applications in integration
  • Practice problems involving the Distributive Property in calculus
  • Explore advanced integration techniques, including reduction formulas
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of common mistakes in solving integration problems.

themadhatter1
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Homework Statement



attachment.php?attachmentid=30843&stc=1&d=1293143474.gif


Homework Equations



The Attempt at a Solution



I tried this problem and couldn't figure it out so I went and got the solution. However, I don't understand step 6 of the solution. I'm not sure how

(n-1)\int\sin^{n-2}x(1-\sin^2x)dx=(n-1)\int\sin^{n-2}dx-(n-1)\int\sin^nx dx
 

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Never mind, I've found my stupid mistake. Distributive Property!
 

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