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math

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Integrate x^2/rootx-1..

  • math - ,

    this one is a bit less complicated than the last one.

    ∫x^2/√(x-1)

    Let u^2 = x-1
    2u du = dx
    x = 1+u^2

    and we have

    ∫(1+u^2)^2/u 2u du
    2∫(1+u^2)^2 du
    2∫1 + 2u^2 + u^4 du
    2(u + 2/3 u^3 + 1/5 u^5)
    2/15 √(x-1)(15 + 10(x-1) + 3(x-1)^2)
    2/15 √(x-1)(15 + 10x - 10 + 3x^2 - 6x + 3)
    2/15 √(x-1) (3x^2 + 4x + 8)

  • math - ,

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