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Math Help - Integration problem

  1. #1
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    Integration problem

    Hello, I'm having difficulties with this indefinite integral:

    (t^2)(e^4t) dt. Do I use a u/v substitution for this?

    Thanks,

    ~CC


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  2. #2
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    Quote Originally Posted by calvin_coolidge View Post
    Hello, I'm having difficulties with this indefinite integral:

    (t^2)(e^4t) dt. Do I use a u/v substitution for this?

    Thanks,

    ~CC
    First do integration by parts: u=t^2 \Longrightarrow u'=2t\,,\,\,v'=e^{4t} \Longrightarrow v=\frac{1}{4}e^{4t}

    After this do ANOTHER integration by parts...and then you're left with an easy exponential integral.

    Tonio
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by calvin_coolidge View Post
    Hello, I'm having difficulties with this indefinite integral:

    (t^2)(e^4t) dt. Do I use a u/v substitution for this?

    Thanks,

    ~CC

    let v=t^2 and du = e^4t dv=2t and u=e^4t/4

    \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 - \int t\frac{e^{4t}}{2} dt

    use derive by part again for the integral let

    v=t and du=e^4t dv=1 and u=e^4t/4

    \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 -(t \frac{e^{4t}}{8} - \int \frac{e^{4t}}{8}dt)

    \int t^2 e^{4t} dt = \frac{e^{4t}}{4} t^2 -t \frac{e^{4t}}{8} + \frac{e^{4t}}{32} +c
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