In Schaum's outline "Mathematical Handbook of Formulas and tables" in the chapter on indefinite integrals (chap 17 of the 1999 copyright version) once and a while two solutions are provided. For example in the section of "integrals involving sinax and cosax" on page 89, integral number 17.19.22 has two solutions. Am I correct to say these are two different solutions? Or are they solutions under different cases? It appears they are different (unless I am messing something up when I evaluate them...). Please clarify this for me if you can. Google books has a preview of the page in question http://books.google.com/books?id=jIMHMX ... &q&f=false.

Thanks.

## multiple solutions in schaum's outline

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### Re: multiple solutions in schaum's outline

At a glance, it looks like they're solutions for different cases (namely for r^2>p^2+q^2 and r^2<p^2+q^2). edit: Initially looked at a different example of something giving more than one solution , where p^2>q^2 or vice versa was what mattered.

I'm surprised they don't specify that somewhere though, as it may not always be obvious what the differing cases are, and whether q^2=p^2 requires a different formula entirely, or if one or both simplifies down to the same thing in that instance. edit: Your specific example does mention what to do in the case they're equal.

I'm surprised they don't specify that somewhere though, as it may not always be obvious what the differing cases are, and whether q^2=p^2 requires a different formula entirely, or if one or both simplifies down to the same thing in that instance. edit: Your specific example does mention what to do in the case they're equal.

Last edited by Dopefish on Wed Jun 08, 2011 5:57 pm UTC, edited 2 times in total.

### Re: multiple solutions in schaum's outline

They are solutions in different cases, depending on the sign of the expression under the radical. One is for r^2 > p^2 + q^2, the other for r^2 < p^2 + q^2.

### Re: multiple solutions in schaum's outline

I agree, that makes sense based on what I am playing with now. I numerically evaluated the integral for a few different cases and it agrees with what you guys are saying. This is what I had guessed was the case (no pun intended) but I wanted to see what some other people thought - it would be nice if Schaum's defined the cases. They must think if anyone wants to carry out such integrals they should know what they are doing... Thanks again.

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