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Can someone please integrate this (hard) (not sure if even possible)

  1. Oct 14, 2012 #1
    Please intergrate: (x+3)/(x^2+4x) is it even possible to integrate this?

    The question in the book was (x+2)/(x^2+4x) and it can nicely be integrated to 0.5ln(x^2+4x), but by changing the 2 to a 3 f'(x) don't go into each other. if you know what i mean.
     
  2. jcsd
  3. Oct 14, 2012 #2
    First:

    $$\frac{1}{x^2+4x}=\frac{1}{4}\left[\frac{1}{x}-\frac{1}{x+4}\right]$$,

    so that

    $$\int\frac{x+3}{x^2+4x}=\frac{1}{2}\int\frac{2x+4}{x^2+4x}dx+\int\frac{1}{x^2+4x}dx=\frac{1}{2}\log(x^2+4x)+\frac{1}{4}\log\left(\frac{x}{x+4}\right)+C$$
     
  4. Oct 14, 2012 #3

    Ray Vickson

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    You are not supposed to do a student's homework---just give hints.

    RGV
     
  5. Oct 14, 2012 #4

    micromass

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    Right. Please just give hints next time and don't solve the entire problem (even if it's not posted in the homework section: if it looks like homework, then don't give full solutions).
     
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