Wolfram alpha gets slowed down and confused by parameters such as "a".
This video shows how to an approach integration that uses a unitless zero parameter approach to get accurate results quickly.
Good tutorial. I also would like to add if you're unsure that if you can extrapolate the general expression from WolframAlpha, sub in other values of a and see if you can figure out the pattern.
Also, you may get Wolfram|Alpha to get Re(1/whatever) > 0 if you include the constants. If you just don't want to test values for 'a', you can just go through the Algebra to get your general expression.
Example: http://imgur.com/XVOCDHd which doing some manipulation would get you
$$ \frac{\3sqrt{\pi}a^{5}}{4} $$
which then can be multiplied with the constant to get the result he got. I think you can even type that into Wolfram with the constant to get the final answer.
Regardless what method that is being used, make sure the integral being typed into Wolfram is accurate. I cannot count how many times I get the wrong answer just because Wolfram misunderstood my integrals. When in doubt, use the method discussed in the video to double check your work.
Good tutorial. I also would like to add if you're unsure that if you can extrapolate the general expression from WolframAlpha, sub in other values of a and see if you can figure out the pattern.
ReplyDeleteAlso, you may get Wolfram|Alpha to get Re(1/whatever) > 0 if you include the constants. If you just don't want to test values for 'a', you can just go through the Algebra to get your general expression.
Example: http://imgur.com/XVOCDHd which doing some manipulation would get you
$$ \frac{\3sqrt{\pi}a^{5}}{4} $$
which then can be multiplied with the constant to get the result he got. I think you can even type that into Wolfram with the constant to get the final answer.
Regardless what method that is being used, make sure the integral being typed into Wolfram is accurate. I cannot count how many times I get the wrong answer just because Wolfram misunderstood my integrals. When in doubt, use the method discussed in the video to double check your work.
That's my two cents.