I prompted Wolfram Alpha with this integration problem:
“integral of (4x^3)/(x^4-8)”
It returns a strange complex result, where it assumes the complex logarithm.
Why does it do this instead of returning the more obvious real result of log(|x^4-8|)? All it is missing is the absolute value.
Am I missing something? I just wanted to report this incase it was an unexpected result.
Thanks
Wolfram Alpha seems to assume that your variable x is complex, instead of real. And it happens that the function log(|x^4-8|) is not a primitive of (4x^3)/(x^4-8) in the complex domain, for the simple reason that the absolute value is not differentiable in the complex sense.
Of course, this advanced calculus fact has always been very confusing for people used to baseic textbook calculus.
