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

[Andy_ToK]

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

 

[christianjb]

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.

 

[Andy_ToK]

hi, thanks. I have the answer but wonder how to solve it without using calculator. Sorry if I wasn't clear.

 

[christianjb]

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).