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I need help solving the integral of t * e^-3t dt

I know that I have to solve using integration by parts and so I've let u=t to rid of dt and dv=e^-3t which I believe would yield -(1/3) * e^-3t as v. Am I doing this correctly?

Thanks. I appreciate the help. (:

  • Calculus -

    Good work. So,

    ∫ u dv = uv - ∫ v du
    = -1/3 t e^-3t - ∫ (-1/3) e^-3t dt

    and you're almost done

  • Calculus -

    Awesome, thanks for the help!

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