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Math Help - Easy u-substitution

  1. #1
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    Easy u-substitution

    integrate 2 / x+3
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  2. #2
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    If it's so easy, why didn't you do it? :O

    Sub u = x+3
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  3. #3
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    why didn't I do it?

    LOL! I think the answer is 2ln|x+3|. It's the constant multiple rule that throws me (which I believe is how that 2 is pulled out). It's easy to operate, but I don't understand it. That is, I do not understand why that 2 can be omitted from integration.
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  4. #4
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    Quote Originally Posted by Retromingent View Post
    LOL! I think the answer is 2ln|x+3|. It's the constant multiple rule that throws me (which I believe is how that 2 is pulled out). It's easy to operate, but I don't understand it. That is, I do not understand why that 2 can be omitted from integration.
    Yes, you are correct, it is 2 \ln | x+3 |.

    Before starting the integral, you should factor out the constants so \int \frac{2}{x+3} = 2\int \frac{1}{x+3}.

    If you are unsure about your answer, differentiate it, \frac{\mathrm{d}(2 \ln | x+3|)}{\mathrm{d}x}, to see if you get the initial integration variable.
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