Integrating Functions with Only One Variable for Beginners

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SUMMARY

The discussion focuses on integrating functions with a single variable, specifically where y is the variable and x and w are constants. The participant is familiar with integration techniques such as substitution, trigonometric substitution, integration by parts, and partial fraction decomposition. They express uncertainty about how to begin the integration process and seek guidance. The response emphasizes the importance of applying various integration methods sequentially to find a solution, reinforcing the learning process through practice.

PREREQUISITES
  • Understanding of basic integration techniques: substitution, trigonometric substitution, integration by parts, and partial fraction decomposition.
  • Familiarity with the concept of constants in integration.
  • Knowledge of function rearrangement for integration purposes.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Practice integrating functions with constants using substitution methods.
  • Explore advanced integration techniques such as integration by parts in more complex scenarios.
  • Learn about the application of trigonometric substitution in integration problems.
  • Study the process of rearranging functions to simplify integration.
USEFUL FOR

Students learning calculus, mathematics educators, and anyone seeking to improve their skills in integrating functions with single variables.

NihalRi
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1. Homework Statement
image.jpg

I'm trying to integrate this, the only variable is y the others(x,w) are all constants.

Homework Equations


The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition.

The Attempt at a Solution


Looking at this I can't think of where I'd begin, should I rearange? Is it multistep? It it possible ? I'd appreciate any help :)
 
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NihalRi said:
1. Homework Statement
View attachment 108595
I'm trying to integrate this, the only variable is y the others(x,w) are all constants.

Homework Equations


The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition.

The Attempt at a Solution


Looking at this I can't think of where I'd begin, should I rearange? Is it multistep? It it possible ? I'd appreciate any help :)

PF rules say that you are required to put in effort and show your work. So, try out the methods you have learned. If Method I does not work, then try Method II. If that does not work, turn to Method III, etc. And yes, indeed, it takes some (possibly wasted) work and uses a lot of (possibly wasted) paper but that is how you will learn.
 
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