How Do You Solve the Integral (1+y^2)/(1-y) dy Using Substitution?

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SUMMARY

The integral of (1+y^2)/(1-y) dy can be solved using the substitution method. Specifically, the substitution 1-y = t simplifies the integral significantly. This approach allows for easier manipulation and integration of the function. Users reported success with this method, confirming its effectiveness in solving the integral.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with substitution methods in integration
  • Knowledge of algebraic manipulation
  • Basic proficiency in handling rational functions
NEXT STEPS
  • Practice solving integrals using substitution techniques
  • Explore advanced integration methods such as integration by parts
  • Learn about improper integrals and their applications
  • Study the properties of rational functions in calculus
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Students and educators in mathematics, particularly those studying calculus and integral techniques. This discussion is also beneficial for anyone looking to enhance their problem-solving skills in integration.

jason.bourne
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how do i solve this integral

integral of [ (1+y^2) / (1-y) ] dy

??

i tried my best but i couldn't solve.
help me out please.
 
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jason.bourne said:
how do i solve this integral

integral of [ (1+y^2) / (1-y) ] dy

??

i tried my best but i couldn't solve.
help me out please.

You say you've tried your best; but you haven't shown exactly what you've tried.

So...what methods have you tried?
 


let u=log(1-y)
 


The first thing I would do is divide that out.
 


This is ridiculous. Obviously Jason Bourne hasn't even bothered to look back at this thread.
 


guys,
m sorry i couldn't reply. i was away for few days.

thank you very very very much for your replies.
i apologize for not replying.

thanks lurflurf ur method did work.
once again sorry for the late response.

thank you guys.
 


Make the substitution

1-y = t. Can you rewrite the integral in terms of 't' ?
 

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