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Math Help - Integrating

  1. #1
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    Integrating

    Intergrate \frac{1}{(2+x)^2} with respect to x


    My attempt : \frac{1}{(2+x)^2}= ln(2+x)^2

    i am having doubts if it is really so simple, i guess i am wrong and am here to clarify
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  2. #2
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    Have you seen partial fractions before?
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  3. #3
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    No need for partial fractions (writing this as "partial fractions" would require \frac{A}{x+ 2}+ \frac{B}{(x+ 2)^2} and you would find that A= 0, B= 1. In other words, you get back exactly what you had.)

    Instead, let u= x+ 2. Then your integral is \int \frac{du}{u^2}= \int u^{-2}du
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  4. #4
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    does this means i do not use ln rule to integrate but rather use normal power rule to intergrate?
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  5. #5
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Punch View Post
    does this means i do not use ln rule to integrate but rather use normal power rule to intergrate?
    No, you do not need the ln rule. Yes, you need the power rule.

    \int \frac{1}{x} dx = ln(x) does NOT mean that \int \frac{1}{x^2} dx = ln(x^2)

    Follow what HallsofIvy has said in the above post.
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