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Thread: integration by parts?

  1. #1
    Oct 2008

    integration by parts?

    I'm sure this is an easy one, but can anyone explain how this is done?

    $\displaystyle \int_{1}^{2} 5ln(3x) dx$

    I believe it's an integration by parts problem, but I'm having trouble deciding what to call u and dv. Thanks. I'm new, so sorry if I broke any understood etiquette! =)
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  2. #2
    Member RedBarchetta's Avatar
    Apr 2008
    United States
    Try pulling out the constant first. Then applying integration by parts, but don't forget to multiply by the constant when you're finished.

    5\int_1^2 {\ln (3x)dx} \Rightarrow \left[ {\begin{array}{*{20}c}
    {u = \ln (3x)} \\
    {dv = dx} \\

    \end{array} } \right] \to \int_a^b {udv} = \left[ {uv} \right]_a^b - \int_a^b {vdu}

    Remember this acronym:

    LIPET: Log Function, Inverse Trig Function, Power Function, Exponential Function, Trig Function

    This helps in how you in choosing u, with the highest priority given in order starting with logs, inverse trig, etc. This should make the selection of u and v easier, as is the goal of the parts method is to make the integral of v du easier than your original integral.
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