Help Evaluating the Integral, U-Substitution?

∫ 1 / (1+x^1/3)dx

Use u=1+x^1/3

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  • 7 years ago
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    u = 1 + x^(1/3)

    u - 1 = x^(1/3)

    (u - 1)^3 = x

    d/du (u - 1)^3 = dx/du

    3(u - 1)^2 = dx/du

    dx = 3(u - 1)^2 du

    integrate 1 / (1 + x^(1/3)) dx

    = integrate (1 / u) * (3)(u - 1)^2 du

    = integrate 3(u^2 - 2u + 1) / u du

    = integrate 3u - 6 + 3/u du

    = (3/2)u^2 - 6u + 3ln(u) + Constant

    = (3/2)(1 + x^(1/3))^2 - 6(1 + x^(1/3)) + 3ln(1 + x^(1/3)) + Constant

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