2.1.21 Integrals 2001 to 2017

2.1.21.1 Fricas [F(-2)]

Exception generated. \[ \int \frac {1-x^3+x^6}{\sqrt [3]{x^2+x^4} \left (-1+x^6\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((x^6-x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (re
sidue poly has multiple non-linear factors)

input file name 9_Blake_problems/BlakeProblems.txt

Test file number \(209\)

Integral number in file \(3025\)

2.1.21.2 Fricas [F(-2)]

Exception generated. \[ \int \frac {1+x^3+x^6}{\sqrt [3]{x^2+x^4} \left (-1+x^6\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((x^6+x^3+1)/(x^4+x^2)^(1/3)/(x^6-1),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (re
sidue poly has multiple non-linear factors)

input file name 9_Blake_problems/BlakeProblems.txt

Test file number \(209\)

Integral number in file \(3026\)

2.1.21.3 Fricas [F(-2)]

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

[In]

integrate((1+x)/(x^2-3)/(x^2+1)^(1/3),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (tr
ace 0)

input file name 9_Blake_problems/BlakeProblems.txt

Test file number \(209\)

Integral number in file \(3056\)

2.1.21.4 Fricas [F(-2)]

Exception generated. \[ \int \frac {1+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((1+x)/(8*x^8+84*x^7+338*x^6+679*x^5+825*x^4+784*x^3+522*x^2+189*x+27)^(1/3),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (re
sidue poly has multiple non-linear factors)

input file name 9_Blake_problems/BlakeProblems.txt

Test file number \(209\)

Integral number in file \(3070\)

2.1.21.5 Fricas [F(-2)]

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

[In]

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

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (tr
ace 0)

input file name 9_Blake_problems/BlakeProblems.txt

Test file number \(209\)

Integral number in file \(3072\)

2.1.21.6 Fricas [F(-2)]

Exception generated. \[ \int \frac {\left (e^x \log \left (\log \left (e^{x+x^2}-e^x x\right )\right )\right )^{2/9} \left (-4-4 x+e^{x^2} (4+8 x)+\left (4 e^{x^2}-4 x\right ) \log \left (e^{x+x^2}-e^x x\right ) \log \left (\log \left (e^{x+x^2}-e^x x\right )\right )\right )}{\left (9 e^{x^2}-9 x\right ) \log \left (e^{x+x^2}-e^x x\right ) \log \left (\log \left (e^{x+x^2}-e^x x\right )\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((4*exp(x^2)-4*x)*log(exp(x)*exp(x^2)-exp(x)*x)*log(log(exp(x)*exp(x^2)-exp(x)*x))+(8*x+4)*exp(x^2)-
4*x-4)*(exp(x)*log(log(exp(x)*exp(x^2)-exp(x)*x)))^(2/9)/(9*exp(x^2)-9*x)/log(exp(x)*exp(x^2)-exp(x)*x)/log(lo
g(exp(x)*exp(x^2)-exp(x)*x)),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(833\)

2.1.21.7 Fricas [F(-2)]

Exception generated. \[ \int \frac {-6-3 e^x+e^{\frac {1}{3} \left (3 x+\log \left (2+e^x-\log \left (\frac {5}{2}\right )\right )\right )} \left (6+4 e^x-3 \log \left (\frac {5}{2}\right )\right )+3 \log \left (\frac {5}{2}\right )+\left (-6-3 e^x+3 \log \left (\frac {5}{2}\right )\right ) \log (x)}{6+3 e^x-3 \log \left (\frac {5}{2}\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((4*exp(x)+3*log(2/5)+6)*exp(1/3*log(exp(x)+log(2/5)+2)+x)+(-3*exp(x)-3*log(2/5)-6)*log(x)-3*exp(x)-
3*log(2/5)-6)/(3*exp(x)+3*log(2/5)+6),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(975\)

2.1.21.8 Fricas [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{3} \left (-e^{-4+\sqrt [4]{x}}-3 x \log (3)\right )} \left (-e^{-4+\sqrt [4]{x}} \sqrt [4]{x}-12 x \log (3)\right )}{48 x} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/48*(-x^(1/4)*exp(x^(1/4)-4)-12*x*log(3))*exp(-1/3*exp(x^(1/4)-4)-x*log(3))/x,x, algorithm="fricas"
)

[Out]

Exception raised: TypeError >>  Error detected within library code:   alglogextint: unimplemented

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(2446\)

2.1.21.9 Fricas [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{2} \left (-10+\log \left (15-12 x \log \left (2+\log ^2\left (4+x^2\right )\right )\right )\right )} \left (8 x^2 \log \left (4+x^2\right )+\left (16+4 x^2+\left (8+2 x^2\right ) \log ^2\left (4+x^2\right )\right ) \log \left (2+\log ^2\left (4+x^2\right )\right )\right )}{-40-10 x^2+\left (-20-5 x^2\right ) \log ^2\left (4+x^2\right )+\left (32 x+8 x^3+\left (16 x+4 x^3\right ) \log ^2\left (4+x^2\right )\right ) \log \left (2+\log ^2\left (4+x^2\right )\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((2*x^2+8)*log(x^2+4)^2+4*x^2+16)*log(log(x^2+4)^2+2)+8*x^2*log(x^2+4))*exp(1/2*log(-12*x*log(log(x
^2+4)^2+2)+15)-5)/(((4*x^3+16*x)*log(x^2+4)^2+8*x^3+32*x)*log(log(x^2+4)^2+2)+(-5*x^2-20)*log(x^2+4)^2-10*x^2-
40),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(3878\)

2.1.21.10 Fricas [F(-2)]

Exception generated. \[ \int \frac {e^{2 e^{\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )}+\frac {1}{3} \left (-3+\log \left (\frac {e^4 x+x^2-3 x \log (x)}{e^4+x}\right )\right )} \left (-2 e^8+e^4 (6-4 x)+6 x-2 x^2+6 e^4 \log (x)\right )}{-3 e^8 x-6 e^4 x^2-3 x^3+\left (9 e^4 x+9 x^2\right ) \log (x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((6*exp(4)*log(x)-2*exp(4)^2+(6-4*x)*exp(4)-2*x^2+6*x)*exp(1/3*log((-3*x*log(x)+x*exp(4)+x^2)/(x+exp(
4)))-1)*exp(2*exp(1/3*log((-3*x*log(x)+x*exp(4)+x^2)/(x+exp(4)))-1))/((9*x*exp(4)+9*x^2)*log(x)-3*x*exp(4)^2-6
*x^2*exp(4)-3*x^3),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   do_alg_rde: unimplemented kernel

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(5066\)

2.1.21.11 Fricas [F(-2)]

Exception generated. \[ \int \frac {\left (20 x^2-4 x^4\right ) \log \left (5-x^2\right )+\left (-10 x^3+2 x^5\right ) \log \left (5-x^2\right ) \log \left (\log \left (5-x^2\right )\right )+\sqrt {2-x \log \left (\log \left (5-x^2\right )\right )} \left (2 x^3+\left (-20+4 x^2\right ) \log \left (5-x^2\right )+\left (5 x-x^3\right ) \log \left (5-x^2\right ) \log \left (\log \left (5-x^2\right )\right )\right )}{\left (20 x^2-4 x^4\right ) \log \left (5-x^2\right )+\left (-10 x^3+2 x^5\right ) \log \left (5-x^2\right ) \log \left (\log \left (5-x^2\right )\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-x^3+5*x)*log(-x^2+5)*log(log(-x^2+5))+(4*x^2-20)*log(-x^2+5)+2*x^3)*(-x*log(log(-x^2+5))+2)^(1/2
)+(2*x^5-10*x^3)*log(-x^2+5)*log(log(-x^2+5))+(-4*x^4+20*x^2)*log(-x^2+5))/((2*x^5-10*x^3)*log(-x^2+5)*log(log
(-x^2+5))+(-4*x^4+20*x^2)*log(-x^2+5)),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(5285\)

2.1.21.12 Fricas [F(-2)]

Exception generated. \[ \int \frac {e^{\sqrt {\frac {200-25 \log \left (e^x x\right )}{x}}} \left (16+\sqrt {\frac {200-25 \log \left (e^x x\right )}{x}} \left (9+x-\log \left (e^x x\right )\right )-2 \log \left (e^x x\right )\right )}{-16 x^2+2 x^2 \log \left (e^x x\right )} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-log(exp(x)*x)+x+9)*((-25*log(exp(x)*x)+200)/x)^(1/2)-2*log(exp(x)*x)+16)*exp(((-25*log(exp(x)*x)+
200)/x)^(1/2))/(2*x^2*log(exp(x)*x)-16*x^2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   do_alg_rde: unimplemented kernel

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(5642\)

2.1.21.13 Fricas [F(-2)]

Exception generated. \[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-10*x*exp(3)-50)*exp((x^2*exp(3)^2+10*x*exp(3)+25)/x^2)*log(x)+x^2*exp((x^2*exp(3)^2+10*x*exp(3)+
25)/x^2)-x^3)*exp(1/3*log(exp((x^2*exp(3)^2+10*x*exp(3)+25)/x^2)*log(x)-x)-5/3)+3*x^3*exp((x^2*exp(3)^2+10*x*e
xp(3)+25)/x^2)*log(x)-3*x^4)/(3*x^3*exp((x^2*exp(3)^2+10*x*exp(3)+25)/x^2)*log(x)-3*x^4),x, algorithm="fricas"
)

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

input file name 10_Hebisch/Hebisch_Problems.txt

Test file number \(210\)

Integral number in file \(8482\)

2.1.21.14 Fricas [F(-2)]

Exception generated. \[ \int (1-x)^{2014} x \, dx=\text {Exception raised: RuntimeError} \]

[In]

integrate(x*(1-x)^2014,x, algorithm="fricas")

[Out]

Exception raised: RuntimeError >>  System error:   Heap exhausted (no more space for allocation).2293760 bytes
available, 2557536 requested.PROCEED WITH CAUTION.

input file name 11_MIT/MIT_bee_problems.txt

Test file number \(211\)

Integral number in file \(105\)

2.1.21.15 Fricas [F(-2)]

Exception generated. \[ \int (1-x)^{2020} x \, dx=\text {Exception raised: RuntimeError} \]

[In]

integrate(x*(1-x)^2020,x, algorithm="fricas")

[Out]

Exception raised: RuntimeError >>  System error:   Heap exhausted (no more space for allocation).1998848 bytes
available, 2179456 requested.PROCEED WITH CAUTION.

input file name 11_MIT/MIT_bee_problems.txt

Test file number \(211\)

Integral number in file \(227\)

2.1.21.16 Fricas [F(-2)]

Exception generated. \[ \int \sqrt {\frac {\log \left (\frac {1}{x}\right )}{x}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((log(1/x)/x)^(1/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

input file name 11_MIT/MIT_bee_problems.txt

Test file number \(211\)

Integral number in file \(259\)

2.1.21.17 Fricas [F(-2)]

Exception generated. \[ \int \left (\frac {1}{\sqrt {2} \sqrt {\log (x)}}+\sqrt {2} \sqrt {\log (x)}\right ) \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(2^(1/2)*log(x)^(1/2)+1/2*2^(1/2)/log(x)^(1/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

input file name 11_MIT/MIT_bee_problems.txt

Test file number \(211\)

Integral number in file \(302\)