Integrate x^3/(x^5-1): Solutions

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Discussion Overview

The discussion centers around the integration of the function x^3/(x^5-1). Participants explore methods for solving this integral, including the use of computational tools versus manual techniques.

Discussion Character

  • Homework-related, Debate/contested, Exploratory

Main Points Raised

  • One participant presents a complex answer to the integral, suggesting it can be computed using a specific format.
  • Another participant expresses a desire to solve the integral without a calculator, indicating a preference for manual methods.
  • A third participant questions the feasibility of solving the integral by hand, suggesting it may be overly complex and recommending the use of Mathematica instead.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the integral can be easily solved by hand, with differing opinions on the complexity of the problem.

Contextual Notes

There are unresolved assumptions regarding the methods available for solving the integral and the definitions of complexity in this context.

Andy_ToK
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Hi, here is the question
integrate x^3/(x^5-1)
 
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Hi, here is the answer:

(2 Sqrt[2 (5 + Sqrt[5])]

1 - Sqrt[5] + 4 x
ArcTan[---------------------] +
Sqrt[2 (5 + Sqrt[5])]

2 Sqrt[10 - 2 Sqrt[5]]

1 + Sqrt[5] + 4 x
ArcTan[--------------------] +
Sqrt[10 - 2 Sqrt[5]]

4 Log[-1 + x] +

(-1 + Sqrt[5])

(-1 + Sqrt[5]) x 2
Log[1 - ---------------- + x ] -
2

(1 + Sqrt[5])

(1 + Sqrt[5]) x 2
Log[1 + --------------- + x ]) / 20
2Edit: The format didn't come out too well. Go to http://integrals.wolfram.com/index.jsp and do it yourself.
 
hi, thanks. I have the answer but wonder how to solve it without using calculator. Sorry if I wasn't clear.
 
Does it look like it would be easy?

My advice- leave it to Mathematica unless you have a pathological interest in doing near-impossible integrals (like GibZ).
 

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