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Math Help - Integration of ∫e^(1/2t) t^2

  1. #1
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    Integration of ∫e^(1/2t) t^2

    How do you integrate ∫[e^(1/2t) t^2]?

    Is this done by parts? I've been away from calculus for about 7 years now...I've been looking through my Calc book but I can't remember very much of this stuff and how to decide what to use to integrate what.
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  2. #2
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    ∫e^(1/2t) t^2

    Use integration by parts twice.

    u=t^2 ----- v=e^(1/2t)
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  3. #3
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    ah great! thanks
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  4. #4
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    Thanks for the help, how does this look?

    1st time by parts:

    u = t^2 dv = e^(1/2t) dt
    du = 2t dt v = 2e^(1/2t)

    uv - Int v du
    = (t^2)(2e^(1/2t)) - Int [2e^(1/2t)](2t) dt

    2nd time by parts:

    u = 2t dv = 2e^(1/2t)
    du = 2t dt v = 4e^(1/2t) dt

    uv - Int v du
    = (2t)(4e^(1/2)) - Int (4e^(1/2t))*2 dt
    = (2t)(4e^(1/2)) - 8*(2e^(1/2t)
    = (2t)(4e^(1/2)) - 16 e^(1/2t)

    Also, sorry but does anyone know where I can find the explanation page? I'm trying to figure out how to display the Integral sign and exponents properly.

    Many thanks
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  5. #5
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    nm, got it
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  6. #6
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    Quote Originally Posted by crabchef
    Also, sorry but does anyone know where I can find the explanation page? I'm trying to figure out how to display the Integral sign and exponents properly.

    Many thanks
    Look around here: http://www.mathhelpforum.com/math-help/latex-help/

    Good luck
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