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Math Help - Integration & Logarithm

  1. #1
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    Integration & Logarithm

    As I do not know anyone fresh enough with Calculus, certainly this forum (that I just joined) is my best destination.

    I studied calculus nearly ~20+ years ago. I nearly forgot everything...

    Here is my problem

    After a few manipulations the integrand I'm dealing with comes out as product of two functions which are (independently) the derivative of the denominator logarithm.
    That means (being D=d/dx):

    Dln(x+1) = [1/(x+1)]
    Dln(x+2) = [1/(x+2)]

    The integral I'm trying to resolve is:

    (integral of) [1/(x+1)] * [1/(x+2)] dx

    Iím now stuck because I cannot recall at all how to find the primitive, i.e. how to resolve the integral. I believe it should be resolved integrating by parts. Right?

    Could someone please guide me through?
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Rewrite it as

    \int\frac{1}{x+1}dx-\int\frac{1}{x+2}dx
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  3. #3
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    Thanks, but I'm not sure what you mean.

    The function to be integrated is the product of the two, not the sum...


    Quote Originally Posted by galactus View Post
    Rewrite it as

    \int\frac{1}{x+1}dx-\int\frac{1}{x+2}dx
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    He actually splitted the original integrand into two fractions:

    \frac{1}<br />
{{(x + 1)(x + 2)}} = \frac{{(x + 2) - (x + 1)}}<br />
{{(x + 1)(x + 2)}} = \frac{1}<br />
{{x + 1}} - \frac{1}<br />
{{x + 2}}.
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