Definite Integral with u/du subsitition

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SUMMARY

The discussion centers on evaluating an indefinite integral using the u-substitution method, as demonstrated in a textbook example. The user expresses confusion regarding the treatment of the coefficient '2' in front of the term u1/2. Participants clarify that the coefficient should remain during integration, allowing for the integration of both terms with respect to du. This guidance emphasizes the importance of maintaining coefficients throughout the integration process for accurate results.

PREREQUISITES
  • Understanding of u-substitution in calculus
  • Familiarity with indefinite integrals
  • Basic knowledge of integration techniques
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Review the method of u-substitution in calculus textbooks
  • Practice integrating functions with coefficients using various examples
  • Explore advanced integration techniques, such as integration by parts
  • Learn about common pitfalls in integration and how to avoid them
USEFUL FOR

Students studying calculus, particularly those learning integration techniques, and educators seeking to clarify the u-substitution method for their students.

Knight226
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Homework Statement


Evaluate the indefinite integral by the method shown in Example 5. (the example in the book is just using the u and du substitution)

MathHelp1-1.jpg


Homework Equations


None.

The Attempt at a Solution



The question is right below the instruction and after that question is my steps. Please correct me if I have made mistake somewhere along the way or if I am doing it incorrectly. I get stuck at the last step because I am not sure what I should do to the 2 in front of u^1/2. Please help. Thank you very much.

I don't know how to use the math codes in the forum... so I am attaching a screen shot instead. Thank you.

MathHelp1.jpg
 
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The substitution went just fine. I'm not sure what you want to do with the '2'. Just leave it there and try to integrate both terms du. Can you do that?
 
Thank you.
I apologize for my careless. I got confused with the book example >.<.
 

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