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Solve integration using u substitution of (x+1)sqrt(2-x)dx

  • Math -

    integrate (x+1)sqrt(2-x)dx
    u = (sqrt(2 - x))
    u^2 = 2 - x
    x = 2 - u^2
    - 2u du = dx
    I = integral sign

    I (2 - u^2 + 1)u -2u du
    I (3 - u^2)-2u^2 du
    I (-6u^2 + 2u^4) du

    -6 I u^2 du + 2 I u^4 du
    2 I u^4 du - 6 I u^2 du

    2 (1/5 u^5) - 6 (1/3 u^3)
    2/5 u^5 - 2u^3

    substitute back in for u = (sqrt(2-x))

    2/5(sqrt(2-x))^5 - 2(sqrt(2-x))^3

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