# Integration of an inverse function

1. Jan 8, 2009

### iceman_ch

1. The problem statement, all variables and given/known data

$$\int\frac{4}{x(x+3)}$$

2. Relevant equations

3. The attempt at a solution

I can get to s certain point and I know I need to do substitution but, everytime I try a substitution it just creates a more difficult problem.

$$4\int(x^{-1}(x+3)^{-1})$$

I've tried substitution x^-1 for U and using (x+3)^-1 for dv but, none of it works. If someone could give me a gentle nudge it would be appreciated.

Thanks

2. Jan 8, 2009

### gabbagabbahey

This problem is an ideal candidate for the method of "partial fractions".

Try decomposing $$\frac{1}{x(x+3)}$$ into the form $$\frac{A}{x}+\frac{B}{x+3}$$ where A and B are constants you need to determine.

3. Jan 8, 2009

### iceman_ch

OH man so obvious. Your the man thank you so much. I havn't had a math class in over a year and now I'm taking diff eq. Bad idea you should definetly keep them all together.

4. Jan 8, 2009

### HallsofIvy

Staff Emeritus
And, when talking about functions, be careful to distinguish between "reciprocal" and "inverse" functions!