How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by parts but I'm going in circles yet again...

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  1. Let w = 2x^3
    6x^2 dx = dw
    The integral becomes the integral of
    (1/6)w cos w, which can be solved using integration by parts to give
    (1/6)[cos w + w sin w]
    = (1/6)[cos(2x^3) + 2x^2 sin(2x^3)]

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  2. Wouldn't it simply be
    (1/6)sin(2x^3) + c ?

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  3. The derivative of Reiny's answer is
    (1/6)cos(2x^3)*6x^2 = x^2 cos(2x^3), so I must have made a mistake somewhere.

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