# Question:Error, (in SumTools:-DefiniteSum:-ClosedForm) numeric exception: division by zero in Maple 2021.1

## Question:Error, (in SumTools:-DefiniteSum:-ClosedForm) numeric exception: division by zero in Maple 2021.1

Maple 2021

In Maple 2021.1

restart;
int(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x)

gives

Error, (in SumTools:-DefiniteSum:-ClosedForm) numeric exception: division by zero

But in Maple 2020.2 it works OK giving an answer. (A very long one)

3/4*arcsin(2/3*sin(x)*3^(1/2))-3/4*arctan(sin(x)/(-1+4*cos(x)^2)^(1/2))-3/4*arctan(sin(x)/(-1+8*cos(x)^2)^(1/2
))+5/8*arcsin(2/7*sin(x)*14^(1/2))*2^(1/2)-1/2*sin(x)*(-1+4*cos(x)^2)^(1/2)-1/2*sin(x)*(-1+8*cos(x)^2)^(1/2)

Is this a known issue? I know Maple int has went some changes and improvements in Maple 2021 from the release notes. May be this was caused by some of these changes?

https://www.maplesoft.com/products/maple/new_features/

• Integration has been enhanced with improved algorithms for indefinite integration, and the ability to easily specify which integration method should be used and to compare the results from different methods."

Maple 2021.1 on windows 10

update July 2, 2021

These are additional failed integration in 2021.1 that throw exceptions now. no errors in 2020.2

#427
int(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x)

#533 #no error in Maple 2020, it does not evaluate there. But no error
int((-3+exp(7*x))^(2/3)/exp(2*x),x)

#26/11 #no error in Maple 2020, it does not evaluate there. But no error
int((b*x+(b^2*x^2+a)^(1/2))^(1/2)/(b^2*x^2+a)^(1/2),x)

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