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Math Help - integral by parts

  1. #1
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    integral by parts

    Hey All,

    How would you solve the following integral: (by using integration by parts)

    -∫4x^2cosxdx

    ∫udv = uv -∫vdu

    Thank you
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  2. #2
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    Hello, dadon!

    How would you solve the following integral: (by using integration by parts)

    . . -
    4xcos xdx

    First, take out the "-4" and leave it out front: .-4
    xcos xdx

    There is a "tabular" method, but I'll do it the long way . . .


    We must do "by parts" twice.

    Let u = x . . . dv = cos xdx
    . . du = 2xdx . .v = sin x

    And we have: .xsin x - 2
    xsin xdx


    We do "by parts" on this new integral.

    Let u = x . . . dv = sin xdx
    . . du = dx . . .v = -cos x

    And we have: .xsin x -2
    [-xcos x + cos xdx]

    . . . . . . . .= . xsin x + 2xcos x - 2
    cos xdx

    . . . . . . . .= . xsin x + 2xcos x - 2sin x + C


    Don't forget to replace the "-4".

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