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Calculus

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Evaluate integral of x times the square root of (x-4) dx

I got u-(8u^(3/2) over 3)
Can anyone check this for me?

  • Calculus - ,

    if u^2 = x-4
    2u du = dx
    x = u^2+4

    ∫x√(x-4) dx = ∫(u^2+4)u 2u du
    = ∫2u^4 + 8u^2 du
    = 2/5 u^5 + 8/3 u^3
    = u^3 (2/5 u^2 + 8/3)
    = (x-4)^(3/2) (2/5 (x-4) + 8/3)
    = 2/15 (x-4)^(3/2) (3x+8)

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