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Question: Why Can't Maple Evaluate a "Simple" Antiderivative?

Question:Why Can't Maple Evaluate a "Simple" Antiderivative?

DJJerome1976 540 Maple 2019
integration
August 11 2019
0

I am playing around with certain "simple" integrals, and came across this strange behavior in Maple. Maple is able to integrate sin(x)^(1/2)*cos(x)^3, but not sin(x)^(1/3)*cos(x)^3. Any idea why?

trig_integral.mw
 

int(sin(x)^(1/2)*cos(x)^3, x)

-(2/7)*sin(x)^(7/2)+(2/3)*sin(x)^(3/2)

 (1)

int(sin(x)^(1/3)*cos(x)^3, x)

int(sin(x)^(1/3)*cos(x)^3, x)

 (2)

 
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