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Interesting Integral Illation (Posted on 2023-04-06)

Evaluate this definite integral:

 n
 ∫ x²*(1+x⁴)^-1 dx
1/n

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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