There is no closed form expression for that integral that I have been able to find. You will need to use numeric integration.
Note: using floating point powers in an integral is always a problem. Does 1.2 mean 6/5 or 12/10 or something else? The results are different depending on which representation of the power that you choose. If you use a floating point representation then the results are defined in terms of complex logs that will give complex numbers for negative arguments even in cases where we would normally find a negative real root. For example, (-8)^0.333333 is a complex number, whereas (-8)^(1/3) could be -2
