The function integral ((ln x)^2.3) dx can be defined for values of x equal to or greater than 1. This function can be treated as a definite integral and evaluated approximately using a method such as Simpson's Rule.
Using Simpson's Rule on a programmable calculator the integral was found to have a value of 2111 between the limits 100 and 1, using 50 increments.
Normally I would be the last to try to pit a programmable calculator against the might of Mathcad!!
However it is very simple to use a programmable calculator that is pre-programmed with Simpson's rule (such as Sharp model EL-5120). Evaluating the function integral ( [ln x]^2.3 . dx ) between the limits 10^5 and 1 on the EL-5120, with its default of 100 increments, and with Mathcad PLUS 6.0 gave the same result ( 2.268 * 10^7 ) to three decimal places. The EL-5120 took 45 seconds versus the instantaneous result with Mathcad.
The number of increments can be specified by the user on the EL-5120.
The EL-5120 gives an error code if the lower limit of the definite integral of the above-mentioned function is set below 1, the reason being it cannot handle the resulting complex number. This does not seem to me to be a problem in the evaluation of a function that I would expect to be integrated with a lower limit equal to or greater than 1.
