Integrals 3801 to 3900

Maxima [F(-2)]

Exception generated. \[ \int \frac {x \left (1+a+a^2+x^2+a x^2+b x^2+2 a b x^2+b x^4+b^2 x^4\right )}{\left (1+x^2\right ) \left (a+b x^2\right )^{5/2}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x*(b^2*x^4+b*x^4+2*a*b*x^2+a*x^2+b*x^2+a^2+x^2+a+1)/(x^2+1)/(b*x 
^2+a)^(5/2),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for m 
ore detail
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/150_1.6.2

Test file number \(150\)

Integral number in file \(195\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {-1+x^2}{\sqrt {a-b+\frac {b}{x^2}} x^3} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((x^2-1)/(a-b+b/x^2)^(1/2)/x^3,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for m 
ore detail
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/154_1.6.7

Test file number \(154\)

Integral number in file \(137\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {-1+x^2}{\sqrt {a+b \left (-1+\frac {1}{x^2}\right )} x^3} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((x^2-1)/(a+b*(-1+1/x^2))^(1/2)/x^3,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a-4*b>0)', see `assume?` for m 
ore detail
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/154_1.6.7

Test file number \(154\)

Integral number in file \(138\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {a+b x+c x^2}{(d+e x)^3 \sqrt {-1+x^2}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((c*x^2+b*x+a)/(e*x+d)^3/(x^2-1)^(1/2),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume((e-d)*(e+d)>0)', see `assume?` f 
or more de
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/154_1.6.7

Test file number \(154\)

Integral number in file \(156\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{\sqrt {(a+b x) (c+d x)}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/((b*x+a)*(d*x+c))^(1/2),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for m 
ore detail
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/154_1.6.7

Test file number \(154\)

Integral number in file \(315\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{\sqrt {(a+b x) (c-d x)}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/((b*x+a)*(-d*x+c))^(1/2),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for m 
ore detail
 

input file name test_cases/rubi_tests/1_Algebraic_functions/1.6_Miscellaneous/154_1.6.7

Test file number \(154\)

Integral number in file \(316\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{a+b e^x+c e^{2 x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(a+b*exp(x)+c*exp(2*x)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(432\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x}{a+b e^x+c e^{2 x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x/(a+b*exp(x)+c*exp(2*x)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(437\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x^2}{a+b e^x+c e^{2 x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x^2/(a+b*exp(x)+c*exp(2*x)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(442\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(a+b*f^(d*x+c)+c*f^(2*d*x+2*c)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(444\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(a+b*f^(h*x+g)+c*f^(2*h*x+2*g)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(445\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x/(a+b*f^(d*x+c)+c*f^(2*d*x+2*c)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(447\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x^2}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x^2/(a+b*f^(d*x+c)+c*f^(2*d*x+2*c)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(449\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 g+2 h x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((d+e*f^(h*x+g))/(a+b*f^(h*x+g)+c*f^(2*h*x+2*g)),x, algorithm="ma 
xima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(450\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((d+e*f^(h*x+g))/(a+b*f^(h*x+g)+c*f^(2*h*x+2*g)),x, algorithm="ma 
xima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(451\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{a+b e^{-x}+c e^x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(a+b/exp(x)+c*exp(x)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*b*c-a^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(460\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x}{a+b e^{-x}+c e^x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x/(a+b/exp(x)+c*exp(x)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a^2-4*b*c>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(461\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x^2}{a+b e^{-x}+c e^x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x^2/(a+b/exp(x)+c*exp(x)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a^2-4*b*c>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(462\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {1}{a+b f^{-c-d x}+c f^{c+d x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(a+b*f^(-d*x-c)+c*f^(d*x+c)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*b*c-a^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(463\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x}{a+b f^{-c-d x}+c f^{c+d x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x/(a+b*f^(-d*x-c)+c*f^(d*x+c)),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a^2-4*b*c>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(464\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {x^2}{a+b f^{-c-d x}+c f^{c+d x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(x^2/(a+b*f^(-d*x-c)+c*f^(d*x+c)),x, algorithm="maxima")
                                                                                    
                                                                                    
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a^2-4*b*c>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(465\)

Maxima [F(-2)]

Exception generated. \[ \int a^x b^x \, dx=\text {Exception raised: ValueError} \] Input:

integrate(a^x*b^x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(log(b)/log(a)>0)', see `assume?` 
 for more
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(487\)

Maxima [F(-2)]

Exception generated. \[ \int a^x b^{-x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(a^x/(b^x),x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(-log(b)/log(a)>0)', see `assume? 
` for more
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(491\)

Maxima [F(-2)]

Exception generated. \[ \int a^x b^x c^x \, dx=\text {Exception raised: ValueError} \] Input:

integrate(a^x*b^x*c^x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(log(c)/log(a)+log(b)/log(a)>0)', 
 see `assu
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(492\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {\left (d+e e^{h+i x}\right ) (f+g x)^3}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((d+e*exp(i*x+h))*(g*x+f)^3/(a+b*exp(i*x+h)+c*exp(2*i*x+2*h)),x, 
algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(494\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {\left (d+e e^{h+i x}\right ) (f+g x)^2}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((d+e*exp(i*x+h))*(g*x+f)^2/(a+b*exp(i*x+h)+c*exp(2*i*x+2*h)),x, 
algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(495\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {\left (d+e e^{h+i x}\right ) (f+g x)}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((d+e*exp(i*x+h))*(g*x+f)/(a+b*exp(i*x+h)+c*exp(2*i*x+2*h)),x, al 
gorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(496\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {d+e e^{h+i x}}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((d+e*exp(i*x+h))/(a+b*exp(i*x+h)+c*exp(2*i*x+2*h)),x, algorithm= 
"maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for 
 more deta
 

input file name test_cases/rubi_tests/2_Exponentials/155_2_Exponential_functions

Test file number \(155\)

Integral number in file \(497\)

Maxima [F(-2)]

Exception generated. \[ \int F^{c+d \arctan (a+b x)^n} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(F^(c+d*arctan(b*x+a)^n),x, algorithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(13\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{-i \arctan (a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(1+I*(b*x+a))*(1+(b*x+a)^2)^(1/2)/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(208\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{-3 i \arctan (a+b x)}}{x^4} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(1/(1+I*(b*x+a))^3*(1+(b*x+a)^2)^(3/2)/x^4,x, algorithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(229\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{i \arctan (a x)}}{\sqrt {c+a^2 c x^2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(1/2),x, algorithm="ma 
xima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(328\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{-i \arctan (a x)}}{\left (1+a^2 x^2\right )^{3/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(1/(1+I*a*x)/(a^2*x^2+1),x, algorithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(338\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 i \arctan (a x)}}{\left (c+a^2 c x^2\right )^{3/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)/(a^2*c*x^2+c)^(3/2),x, algorithm=" 
maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(344\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{i \arctan (a x)}}{\left (c+a^2 c x^2\right )^{3/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)/(a^2*c*x^2+c)^(3/2),x, algorithm="ma 
xima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(346\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{-2 i \arctan (a x)} x^2}{\left (c+a^2 c x^2\right )^3} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(x^2/(1+I*a*x)^2*(a^2*x^2+1)/(a^2*c*x^2+c)^3,x, algorithm="maxima 
")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(392\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{-4 i \arctan (a x)} x^2}{\left (c+a^2 c x^2\right )^9} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(x^2/(1+I*a*x)^4*(a^2*x^2+1)^2/(a^2*c*x^2+c)^9,x, algorithm="maxi 
ma")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(393\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{5 i \arctan (a x)} x^2}{\left (c+a^2 c x^2\right )^{27/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((1+I*a*x)^5/(a^2*x^2+1)^(5/2)*x^2/(a^2*c*x^2+c)^(27/2),x, algori 
thm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(394\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 i \arctan (a x)} x^2}{\left (c+a^2 c x^2\right )^{11/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((1+I*a*x)^3/(a^2*x^2+1)^(3/2)*x^2/(a^2*c*x^2+c)^(11/2),x, algori 
thm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(395\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{i \arctan (a x)} x^2}{\left (c+a^2 c x^2\right )^{3/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((1+I*a*x)/(a^2*x^2+1)^(1/2)*x^2/(a^2*c*x^2+c)^(3/2),x, algorithm 
="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.4/159_2.4.3

Test file number \(159\)

Integral number in file \(396\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arccosh}(a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/162_2.5.2

Test file number \(162\)

Integral number in file \(5\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arccosh}(a+b x)}}{x^2} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^2,x, algorithm="maxima 
")
                                                                                    
                                                                                    
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/162_2.5.2

Test file number \(162\)

Integral number in file \(6\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arccosh}(a+b x)}}{x^3} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^3,x, algorithm="maxima 
")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/162_2.5.2

Test file number \(162\)

Integral number in file \(7\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arccosh}(a+b x)}}{x^4} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^4,x, algorithm="maxima 
")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/162_2.5.2

Test file number \(162\)

Integral number in file \(8\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arccosh}(a+b x)}}{x^5} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+(b*x+a-1)^(1/2)*(b*x+a+1)^(1/2))/x^5,x, algorithm="maxima 
")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/162_2.5.2

Test file number \(162\)

Integral number in file \(9\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(859\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x^2} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^2,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(860\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x^3} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^3,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(861\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x^4} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^4,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(862\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(876\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x^2} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^2,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(877\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x^3} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^3,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(878\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x^4} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^4,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(879\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{-\text {arctanh}(a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(884\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {arctanh}(a x)} x^2 \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm 
="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(986\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {arctanh}(a x)} x \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=" 
maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(987\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm="ma 
xima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(988\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} x^3 \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorit 
hm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1193\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} x^2 \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorit 
hm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1194\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} x \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm 
="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1195\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=" 
maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1196\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm 
="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1197\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorit 
hm="maxima")
                                                                                    
                                                                                    
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1198\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} \left (c-a^2 c x^2\right )^{3/2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=" 
maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1202\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{3/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1330\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{5/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1331\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{7/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1332\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{9/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/163_2.5.3

Test file number \(163\)

Integral number in file \(1333\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {sech}^{-1}(a x)} x^m \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/x+(-1+1/a/x)^(1/2)*(1+1/a/x)^(1/2))^3*x^m,x, algorithm="max 
ima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(m-3>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/165_2.5.5

Test file number \(165\)

Integral number in file \(40\)

Maxima [F(-2)]

Exception generated. \[ \int e^{2 \text {sech}^{-1}(a x)} x^m \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/x+(-1+1/a/x)^(1/2)*(1+1/a/x)^(1/2))^2*x^m,x, algorithm="max 
ima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(m-2>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/165_2.5.5

Test file number \(165\)

Integral number in file \(41\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {sech}^{-1}\left (a x^3\right )} x^m \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/x^3+(-1+1/a/x^3)^(1/2)*(1/a/x^3+1)^(1/2))*x^m,x, algorithm= 
"maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(m-3>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/165_2.5.5

Test file number \(165\)

Integral number in file \(60\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {sech}^{-1}\left (a x^2\right )} x^m \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/x^2+(-1+1/a/x^2)^(1/2)*(1+1/a/x^2)^(1/2))*x^m,x, algorithm= 
"maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(m-2>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/165_2.5.5

Test file number \(165\)

Integral number in file \(61\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {sech}^{-1}\left (a x^p\right )} x^m \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/(x^p)+(-1+1/a/(x^p))^(1/2)*(1+1/a/(x^p))^(1/2))*x^m,x, algo 
rithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(m-p>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/165_2.5.5

Test file number \(165\)

Integral number in file \(65\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {sech}^{-1}\left (a x^p\right )} x \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/(x^p)+(-1+1/a/(x^p))^(1/2)*(1+1/a/(x^p))^(1/2))*x,x, algori 
thm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(1-p>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/165_2.5.5

Test file number \(165\)

Integral number in file \(66\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {sech}^{-1}\left (a x^p\right )} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/a/(x^p)+(-1+1/a/(x^p))^(1/2)*(1+1/a/(x^p))^(1/2),x, algorithm= 
"maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(-p>0)', see `assume?` for more d 
etails)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/165_2.5.5

Test file number \(165\)

Integral number in file \(67\)

Maxima [F(-2)]

Exception generated. \[ \int e^{2 \text {csch}^{-1}(a x)} x^m \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^m,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(m-2>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/166_2.5.6

Test file number \(166\)

Integral number in file \(21\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {csch}^{-1}\left (a x^2\right )} x^m \, dx=\text {Exception raised: ValueError} \] Input:

integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^m,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(m-2>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/166_2.5.6

Test file number \(166\)

Integral number in file \(35\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(844\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x^2} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^2,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(845\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x^3} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^3,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(846\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\text {arctanh}(a+b x)}}{x^4} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)/(1-(b*x+a)^2)^(1/2)/x^4,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(847\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(861\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x^2} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^2,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(862\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x^3} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^3,x, algorithm="maxima")
                                                                                    
                                                                                    
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(863\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a+b x)}}{x^4} \, dx=\text {Exception raised: ValueError} \] Input:

integrate((b*x+a+1)^3/(1-(b*x+a)^2)^(3/2)/x^4,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(864\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{-\text {arctanh}(a+b x)}}{x} \, dx=\text {Exception raised: ValueError} \] Input:

integrate(1/(b*x+a+1)*(1-(b*x+a)^2)^(1/2)/x,x, algorithm="maxima")
 

Output:

Exception raised: ValueError >> Computation failed since Maxima requested 
additional constraints; using the 'assume' command before evaluation *may* 
 help (example of legal syntax is 'assume(a-1>0)', see `assume?` for more 
details)Is
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(869\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {arctanh}(a x)} x^2 \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorithm 
="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(971\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {arctanh}(a x)} x \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm=" 
maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(972\)

Maxima [F(-2)]

Exception generated. \[ \int e^{\text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)/(-a^2*x^2+1)^(1/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm="ma 
xima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(973\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} x^3 \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x, algorit 
hm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1178\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} x^2 \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x, algorit 
hm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1179\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} x \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x, algorithm 
="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1180\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2),x, algorithm=" 
maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1181\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x, algorithm 
="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1182\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{3 \text {arctanh}(a x)} \sqrt {c-a^2 c x^2}}{x^2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x, algorit 
hm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1183\)

Maxima [F(-2)]

Exception generated. \[ \int e^{3 \text {arctanh}(a x)} \left (c-a^2 c x^2\right )^{3/2} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate((a*x+1)^3/(-a^2*x^2+1)^(3/2)*(-a^2*c*x^2+c)^(3/2),x, algorithm=" 
maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negati 
ve exponent.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1187\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{3/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1315\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{5/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1316\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{7/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(7/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
                                                                                    
                                                                                    
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1317\)

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \text {arctanh}(a x)}}{\left (c-a^2 c x^2\right )^{9/2}} \, dx=\text {Exception raised: RuntimeError} \] Input:

integrate(((a*x+1)/(-a^2*x^2+1)^(1/2))^(1/2)/(-a^2*c*x^2+c)^(9/2),x, algor 
ithm="maxima")
 

Output:

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is un 
defined.
 

input file name test_cases/rubi_tests/2_Exponentials/2.5/167_x2.5.3

Test file number \(167\)

Integral number in file \(1318\)