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Math Help - Antiderivative

  1. #1
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    Antiderivative

    I'm doing integrating by parts, and I came across a question that gave dv= er/2

    Why is the anti-derivative 2er/2 ?


    I know my work is wrong for what I have, and I'm really not sure why it is.
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  2. #2
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    Re: Antiderivative

    Because \left (2e^\frac{r}{2}  \right )'=2\cdot e^\frac{r}{2} \cdot \left ( \frac{r}{2} \right )'=2\cdot e^\frac{r}{2} \cdot \frac{1}{2}=e^\frac{r}{2}.
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  3. #3
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    Re: Antiderivative

    thanks, is it a general rule that any e^r/x antiderivative is x^e/x ??
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    Re: Antiderivative

    You're welcome! ^^

    Uhm, I don't know what you actually wanted to ask, but yes, there is a rule:

    \left (e^{f(x)}  \right )'=f'(x) \cdot e^{f(x)}

    Also, if f(x)=ax+b, then:

    \left (e^{ax+b}  \right )'=a \cdot e^{ax+b}

    So the antiderivate of e^{ax+b} is \frac{1}{a}e^{ax+b}.
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  5. #5
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    Re: Antiderivative

    Quote Originally Posted by Steelers72 View Post
    thanks, is it a general rule that any e^r/x antiderivative is x^e/x ??
    Be careful about using "x" there since it will typically be interpreted as a variable and you mean it as a constant here. It is true that the derivative of e^(ar), with respect to r, where a is a constant, is ae^(ar) so that the derivative of e^(ar)/a, with respect to r, is ae^(ar)/a= e^(ar) so that the antiderivative of e^(ar) (again with constant a) is e^(ar)/a.
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  6. #6
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    Re: Antiderivative

    I see what you mean

    so e^r/constant = constant*e^r/constant ?
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