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Math Help - Antiderivatives

  1. #1
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    Antiderivatives

    Alright, so we're supposed to find the anti derivatives for integration of 2t+e^2t.

    The first anti derivative is 1/3t^3 + 1/2e^2t, but I am not certain how that was found, and then, we're supposed to find the anti derivative of that, and then the anti derivative once more.

    I was wondering if someone could explain how exactly to find antiderivatives in a case like this?
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  2. #2
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    Quote Originally Posted by Mike5055 View Post
    Alright, so we're supposed to find the anti derivatives for integration of 2t+e^2t.

    The first anti derivative is 1/3t^3 + 1/2e^2t, but I am not certain how that was found, and then, we're supposed to find the anti derivative of that, and then the anti derivative once more.

    I was wondering if someone could explain how exactly to find antiderivatives in a case like this?
    I will be stunned if you don't you have these rules in your class notes or textbook:

    \int t^n \, dt = \frac{1}{n} t^{n+1} + C, ~ n \neq -1.

    \int e^{kt} \, dt = \frac{1}{k} e^{kt} + C.

    You're expected to know them.
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