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Integration problem.

  1. Jan 10, 2010 #1
    I understand the mechanics of how this happens but i don't really understand why.


    Why can't the constant be taken out?:confused:
  2. jcsd
  3. Jan 10, 2010 #2
    What makes you think it can't be?
  4. Jan 10, 2010 #3

  5. Jan 10, 2010 #4
    \int 5x

    So, which is right?

    \int 5x = \frac{(5x)^2}{2} + C
    \int 5x = 5\frac{x^2}{2} + C
    Even in regular integration, you always pull off the constants. Just because you have 1/x doesn't mean the constant shouldn't be pulled out.

    However, it does worth mentioning that both your answers are actually right.

    \frac{a}{b}ln(bx+bc)+C = \frac{a}{b}ln(b(x+c))+C = \frac{a}{b}ln(x+c)+ \frac{a}{b}ln b + C = \frac{a}{b}ln(x+c)+D
    Where D is just another constant.
  6. Jan 10, 2010 #5
    I know.
    Ok now I understand it. I actually run into this problem while trying to calculate integration factors for ODEs. This should simplify my calculations.

    Thank you.
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