Solution 17109: Differences in Answers for Anitderivatives on TI-89 Family, TI-92 Family, Voyage™ 200, and TI-Nspire™ CAS Family.
Why is there a difference in antiderivative results on TI -89 family, TI-92 Plus, Voyage 200, TI-Nspire CAS family and the results presented by third party (CAS) tools?
When computing the general antiderivative of a function, there should be an added random constant to the result. CAS packages do not show the constant of integration and only provide one valid antiderivative. Different CAS packages follow slightly different sets of rules, therefore 2 CAS programs may return answers that differ by a constant.
For example: antiderivative of cot(x)*1/(csc(x))^2
The answer received from the TI-89 Titanium is: -1/(2*(sin(x))^2)
Some third party CAS tools may supply an answer such as: -(1/2)*(cot(x))^2
The result is the same with a difference of 1/2.
Each answer is a valid antiderivative of cot(x)*1/(csc(x))^2.