1. ## 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

I’m 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?

2. Rewrite it as

$\int\frac{1}{x+1}dx-\int\frac{1}{x+2}dx$

3. Thanks, but I'm not sure what you mean.

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

Originally Posted by galactus
Rewrite it as

$\int\frac{1}{x+1}dx-\int\frac{1}{x+2}dx$

4. He actually splitted the original integrand into two fractions:

$\frac{1}
{{(x + 1)(x + 2)}} = \frac{{(x + 2) - (x + 1)}}
{{(x + 1)(x + 2)}} = \frac{1}
{{x + 1}} - \frac{1}
{{x + 2}}.$