It is correct. There are two good quick ways to check if the antiderivative your 49 has given you is valid:

One is as stated above, take the derivative and see if you get back the function you started with. That is the classic math approach, is absolutely valid, although some algebraic simplification may be needed for complicated functions.

Another method is to use a second computer algebra system, such as Mathematica or Maple. ( The 49 was originally programmed using Maple, and it's suprising to see how close the 49 is to Maple (versions 6 thru 8) on many things.) Integrate your function with the other CAS, then plugging in small numbers, such as x=1,2,3... and Pi/(8,4,2) for trig functions, see if the functions are equal. I'm impressed at the accuracy of the 49's antiderivatives. There are a number of errors, but relatively few. The math professor who programmed the 49 did a superb job with indefinite integration, using partial implementation of the Risch algorithm.

The TI89 is often mentioned in comparison to the 49 with regards to integration. The TI89 is generally faster but lacks the Risch methods, instead relying on plug and chug heuristics. There are a number of antiderivatives the TI89 can't do the 49 can, and vice versa. The only area where the 89 outperforms the 49 is with multiple integrals, being much faster. In the final result, though, they are both fairly well matched. An engineer is well armed with either one.

As for integration tables, there is really only one that I use, Gradshteyn and Reyshik's Table Of Integrals, Series and Products. While the table is mostly accurate, there are a number of well-known errors found by programmers when testing the integration powers of Mathematica.

*Edited: 19 Nov 2005, 3:10 p.m. *