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In the exercise we want to use a substitution to integrate integral xsqrt(x+1)dx.
Find the substitution u to transform the integral into integral(u-1)u^(1/2)du. u=?

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Natalie

  1. If you take u = x + 1

    Then, x + 1 = u => sqrt(x+1) = sqrt(u) = u^(1/2)

    Then, x = (u - 1)

    And, du/dx = 1 => du = dx

    So,

    x*sqrt(x+1)*dx
    Becomes
    (u-1)*sqrt(u)*du = (u-1)u^(1/2)du

    With the substitution u = x + 1

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    Arora

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