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Integral of 1/(x^2 (x^4 + 1)^(3/4))

The same question, asked 5 times: 2 May 2023 S2, 4 May 2023 S2, 10 May 2023 S2, 10 May 2024 S1, 10 May 2024 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2 May 2023 S2

    115
    The value of I=∫dxx2(x4+1)3/4I = \int \frac{dx}{x^2(x^4+1)^{3/4}} is

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  2. Question 2

    4 May 2023 S2

    117
    The value of ∫dxx2(x4+1)3/4\int\frac{dx}{x^2(x^4+1)^{3/4}} is

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  3. Question 3

    10 May 2023 S2

    144
    The value of ∫dxx2(x4+1)3/4\int\frac{dx}{x^2(x^4+1)^{3/4}} is

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  4. Question 4

    10 May 2024 S1

    110
    If I=∫dxx2(x4+1)3/4I=\int\frac{dx}{x^2(x^4+1)^{3/4}}, then I is

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  5. Question 5

    10 May 2024 S2

    138
    The value of ∫dxx2(x4+1)3/4\displaystyle\int\frac{dx}{x^2(x^4+1)^{3/4}} is

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