Indefinate integration problems

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SUMMARY

The discussion focuses on solving indefinite integrals, specifically the integrals ∫ 6x² / √(2x³ + 9), ∫ x √(1 - x²), and ∫ 4 / ((x + 2)(x + 3)). Participants emphasize the importance of demonstrating prior attempts and understanding integration techniques such as u-substitution. The advice provided encourages learners to engage with the material actively and develop problem-solving skills rather than relying solely on external help.

PREREQUISITES
  • Understanding of indefinite integrals and their notation
  • Familiarity with u-substitution method in calculus
  • Basic knowledge of differentiation techniques
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Practice solving indefinite integrals using u-substitution
  • Explore integration techniques such as integration by parts
  • Study the concept of antiderivatives and their applications
  • Review common integral forms and their derivatives
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Students learning calculus, educators teaching integration techniques, and anyone seeking to improve their problem-solving skills in mathematics.

JakePearson
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Indefinate integration problems!

find the following indefinate integrals?

d) ∫ 6x2 / sqrt(2x3 + 9)
e) ∫ x sqrt(1 - x2
f) ∫ 4 / (x + 2)(x + 3)

can you help me answer these please
 
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You keep posting questions with absolutely no work or ideas. Please post what you've tried, what techniques do you know, what is causing the problem, etc. Review u-substitution in your book, and then post again if you are still stuck. I've seen multiple posts on homework type questions. Whether it's for a class or not, you aren't getting what you need to out of the exercises if you are posting nearly every question and not struggling through it yourself. I'm not trying to be difficult, but I'm trying to force you to try.

Try something! If it doesn't work, then why didn't it work? How can you modify it? These are techniques you have to learn so that you aren't reliant on others to complete your work.
 


Substitution is a good method to try. Another thing that works well for anti derivatives is to try a function that you think may work, differentiate it, and see what you can add to it (constants, etc) to get the desired result. After doing this a while you'll build up your intuition.
 

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