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integration of x^2 * cos^2(x)

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    |x^2*cos^2(x) dx =
    =|x^2*(1/2)(1+cos(2x)) dx
    =(1/2)|x^2 dx + (1/2)|x^2*cos(2x) dx
    =(1/6)x^3 + (1/2)|x^2*cos(2x) dx

    Using integration by part:
    u = x^2
    du = 2x dx
    dv = cos(2x) dx
    v = (1/2) sin(2x)
    |x^2*cos(2x) dx =
    = (1/2)x^2*sin(2x) - |xsin(2x) dx

    Again, using integration by part:
    u = x
    du = dx
    dv = sin(2x) dx
    v = -(1/2)cos(2x)
    |x^2*cos(2x) dx =
    = (1/2)x^2*sin(2x) - {-(1/2)x*cos(2x) + (1/2)|cos(2x) dx}
    = (1/2)x^2*sin(2x) + (x/2)cos(2x) - (1/4)sin(2x) + const

    Finally, we have:
    |x^2*cos^2(x) dx =
    = (1/6)x^3 + (1/4)x^2*sin(2x) + (x/4)cos(2x) - (1/8)sin(2x) + const

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