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Interesting Integral Illation (Posted on 2023-04-06) Difficulty: 3 of 5
Evaluate this definite integral:

 ∫ x2*(1+x4)-1 dx

where n is a real number greater than 1.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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an observation | Comment 1 of 3
If you substitute u = 1/x
The limits become n to 1/n
The integrand becomes  -(1+x^4)^-1
So the original integral is identical to what you get if you delete the x^2 term
∫ 1/n to n: (x^2)(1 + x^4)^(-1) dx
= ∫ 1/n to n: (1 + x^4)^(-1) dx

  Posted by Larry on 2023-04-07 08:43:46
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