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

In summary, the conversation revolves around solving the integral of [ (1+y^2) / (1-y) ] dy. The conversation includes attempts at solving it and suggestions for methods such as making a substitution and dividing out the expression. Ultimately, it is mentioned that the suggested method of substitution successfully solves the integral.
  • #1
jason.bourne
82
1
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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  • #2


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?
 
  • #3


let u=log(1-y)
 
  • #4


The first thing I would do is divide that out.
 
  • #5


This is ridiculous. Obviously Jason Bourne hasn't even bothered to look back at this thread.
 
  • #6


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.
 
  • #7


Make the substitution

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

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

What is an "integral" in mathematics?

An integral is a mathematical concept used to find the area under a curve in a graph. It is also known as "integration" and is a fundamental concept in calculus.

How do I solve an integral?

To solve an integral, you must use integration techniques such as substitution, integration by parts, or partial fractions. You can also use online integral calculators or software programs to help with more complex integrals.

What is the purpose of studying integrals?

Integrals are essential for understanding many mathematical concepts, including areas, volumes, and motion. They are also used in engineering, physics, and other sciences to solve real-world problems.

How can I check if my integral solution is correct?

You can check your integral solution by differentiating it. If the derivative matches the original function, then your solution is correct. You can also use integral tables or online calculators to verify your answer.

What are some tips for solving integrals?

Some tips for solving integrals include: identifying the correct integration technique, understanding the properties of integrals, practicing with different types of integrals, and double-checking your work. It is also helpful to break down the integral into smaller parts and simplify as much as possible.

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