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Math Help - stuck finding antiderivative

  1. #1
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    stuck finding antiderivative

    I'm stuck finding the antiderivative to solve an integral. It's step 6 underlined with a "?".

    I think it should be - ( 1/5 * e^5x * cos9x), then we add the C.
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  2. #2
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    You're not doing the integration by parts correctly. Your derivative of u is incorrect (you need the chain rule), and your integral of dv is incorrect (use a substitution).
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  3. #3
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    make \displaystyle I = \int e^5x\cos 9x ~dx

    As as you have shown integrating by parts twice is the correct method.

    Your derivatives need some attention.

    \displaystyle \int \cos 9x ~dx = \frac{1}{9}\sin 9x

    \displaystyle \frac{d}{dx}( e^5x)=5e^5x
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  4. #4
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    Isn't d/dx of e^5x = e^4x * 5 ?

    Also, I list it as simply du = e^5x dx because my teacher does that for some reason. For instance in the example of e^x he lists it as e^x = e^x dx. So I did the same.. I don't want to learn something the wrong way here I thought my way of showing it was correct.

    So if I were to fix this would the rest be ok?
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  5. #5
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    Quote Originally Posted by solidstatemath View Post
    Isn't d/dx of e^5x = e^4x * 5 ?
    Sorry this is not correct.

    In general

    \displaystyle \frac{d}{dx}(e^{f(x)})= f'(x)e^{f(x)}

    which you are confusing with \displaystyle \frac{d}{dx}(x^n)= nx^{n-1}
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