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Math Help - Integral of (4t-2)*e^(t^2-t).

  1. #1
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    Integral of (4t-2)*e^(t^2-t).

    I wish to integrate (4t-2)*e^(t^2-t).

    U=4t-2
    du/dt = 4

    dv=e^(t^2-t)
    dv/dt = ?

    Am I even on the right track?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Integral of (4t-2)*e^(t^2-t).

    We have:
    \int (4t-2)e^{t^2-t}dt
    which we can write as:
    2\int (2t-1)e^{t^2-t}dt

    Now, let t^2-t=u

    (Do you see why this is a good substitution?)
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  3. #3
    MHF Contributor chisigma's Avatar
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    Re: Integral of (4t-2)*e^(t^2-t).

    What is the derivative of t^{2}-t?... is it somewhere in the integrand function?...



    Marry Christmas from Serbia

    \chi \sigma
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  4. #4
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    Re: Integral of (4t-2)*e^(t^2-t).

    int t^2-t = 2t-1

    Do I then use Integration by parts with dv = ?
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Integral of (4t-2)*e^(t^2-t).

    No, you don't need integration by parts. Have you done substitutions (in integration) before?
    Let t^2-t=u \Rightarrow (2t-1)dt=du

    Do you see how you can use this?
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  6. #6
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    Re: Integral of (4t-2)*e^(t^2-t).

    Thank you people - got it - U substitution.

    2 int (2t-1)*e^(t^2-t) dt
    = 2 int e^u du
    = 2*e^u + c
    = 2*e^(t^2-t) + c
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: Integral of (4t-2)*e^(t^2-t).

    Yes, that's correct.
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