3.29.6 \(\int \frac {(4 x^6+8 x^3 \log (4)) \log (\frac {121 x^4-110 x^5+25 x^6+(110 x^2-50 x^3) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+(4 x^2-2 x^3) \log (4)+\log ^2(4)})+(44 x^5-42 x^6+10 x^7+(42 x^3-20 x^4) \log (4)+10 x \log ^2(4)) \log ^2(\frac {121 x^4-110 x^5+25 x^6+(110 x^2-50 x^3) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+(4 x^2-2 x^3) \log (4)+\log ^2(4)})}{22 x^4-21 x^5+5 x^6+(21 x^2-10 x^3) \log (4)+5 \log ^2(4)} \, dx\)
Optimal. Leaf size=29 \[ x^2 \log ^2\left (\left (-5+\frac {x}{-2 x+x^2-\frac {\log (4)}{x}}\right )^2\right ) \]
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Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[((4*x^6 + 8*x^3*Log[4])*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4
- 4*x^5 + x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)] + (44*x^5 - 42*x^6 + 10*x^7 + (42*x^3 - 20*x^4)*Log[4] + 1
0*x*Log[4]^2)*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4 - 4*x^5 + x^6
+ (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)]^2)/(22*x^4 - 21*x^5 + 5*x^6 + (21*x^2 - 10*x^3)*Log[4] + 5*Log[4]^2),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [C] time = 14.24, size = 57407, normalized size = 1979.55 \begin {gather*} \text {Result too large to show} \end {gather*}
Warning: Unable to verify antiderivative.
[In]
Integrate[((4*x^6 + 8*x^3*Log[4])*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(
4*x^4 - 4*x^5 + x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)] + (44*x^5 - 42*x^6 + 10*x^7 + (42*x^3 - 20*x^4)*Log[
4] + 10*x*Log[4]^2)*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4 - 4*x^5
+ x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)]^2)/(22*x^4 - 21*x^5 + 5*x^6 + (21*x^2 - 10*x^3)*Log[4] + 5*Log[4]^
2),x]
[Out]
Result too large to show
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fricas [B] time = 1.60, size = 80, normalized size = 2.76 \begin {gather*} x^{2} \log \left (\frac {25 \, x^{6} - 110 \, x^{5} + 121 \, x^{4} - 20 \, {\left (5 \, x^{3} - 11 \, x^{2}\right )} \log \relax (2) + 100 \, \log \relax (2)^{2}}{x^{6} - 4 \, x^{5} + 4 \, x^{4} - 4 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \relax (2) + 4 \, \log \relax (2)^{2}}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)*log((100*log(2)^2+2*(-50*x^3+110*x^2
)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)
*log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-
4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+21*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="fricas")
[Out]
x^2*log((25*x^6 - 110*x^5 + 121*x^4 - 20*(5*x^3 - 11*x^2)*log(2) + 100*log(2)^2)/(x^6 - 4*x^5 + 4*x^4 - 4*(x^3
- 2*x^2)*log(2) + 4*log(2)^2))^2
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)*log((100*log(2)^2+2*(-50*x^3+110*x^2
)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)
*log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-
4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+21*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="giac")
[Out]
Timed out
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maple [B] time = 0.71, size = 83, normalized size = 2.86
|
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| method |
result |
size |
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| norman |
\(x^{2} \ln \left (\frac {100 \ln \relax (2)^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \relax (2)+25 x^{6}-110 x^{5}+121 x^{4}}{4 \ln \relax (2)^{2}+2 \left (-2 x^{3}+4 x^{2}\right ) \ln \relax (2)+x^{6}-4 x^{5}+4 x^{4}}\right )^{2}\) |
\(83\) |
| risch |
\(x^{2} \ln \left (\frac {100 \ln \relax (2)^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \relax (2)+25 x^{6}-110 x^{5}+121 x^{4}}{4 \ln \relax (2)^{2}+2 \left (-2 x^{3}+4 x^{2}\right ) \ln \relax (2)+x^{6}-4 x^{5}+4 x^{4}}\right )^{2}\) |
\(83\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((40*x*ln(2)^2+2*(-20*x^4+42*x^3)*ln(2)+10*x^7-42*x^6+44*x^5)*ln((100*ln(2)^2+2*(-50*x^3+110*x^2)*ln(2)+25
*x^6-110*x^5+121*x^4)/(4*ln(2)^2+2*(-2*x^3+4*x^2)*ln(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*ln(2)+4*x^6)*ln((100*ln(2)
^2+2*(-50*x^3+110*x^2)*ln(2)+25*x^6-110*x^5+121*x^4)/(4*ln(2)^2+2*(-2*x^3+4*x^2)*ln(2)+x^6-4*x^5+4*x^4)))/(20*
ln(2)^2+2*(-10*x^3+21*x^2)*ln(2)+5*x^6-21*x^5+22*x^4),x,method=_RETURNVERBOSE)
[Out]
x^2*ln((100*ln(2)^2+2*(-50*x^3+110*x^2)*ln(2)+25*x^6-110*x^5+121*x^4)/(4*ln(2)^2+2*(-2*x^3+4*x^2)*ln(2)+x^6-4*
x^5+4*x^4))^2
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maxima [B] time = 0.61, size = 80, normalized size = 2.76 \begin {gather*} 4 \, x^{2} \log \left (5 \, x^{3} - 11 \, x^{2} - 10 \, \log \relax (2)\right )^{2} - 8 \, x^{2} \log \left (5 \, x^{3} - 11 \, x^{2} - 10 \, \log \relax (2)\right ) \log \left (x^{3} - 2 \, x^{2} - 2 \, \log \relax (2)\right ) + 4 \, x^{2} \log \left (x^{3} - 2 \, x^{2} - 2 \, \log \relax (2)\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)*log((100*log(2)^2+2*(-50*x^3+110*x^2
)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)
*log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-
4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+21*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="maxima")
[Out]
4*x^2*log(5*x^3 - 11*x^2 - 10*log(2))^2 - 8*x^2*log(5*x^3 - 11*x^2 - 10*log(2))*log(x^3 - 2*x^2 - 2*log(2)) +
4*x^2*log(x^3 - 2*x^2 - 2*log(2))^2
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\left (2\,\ln \relax (2)\,\left (42\,x^3-20\,x^4\right )+40\,x\,{\ln \relax (2)}^2+44\,x^5-42\,x^6+10\,x^7\right )\,{\ln \left (\frac {2\,\ln \relax (2)\,\left (110\,x^2-50\,x^3\right )+100\,{\ln \relax (2)}^2+121\,x^4-110\,x^5+25\,x^6}{2\,\ln \relax (2)\,\left (4\,x^2-2\,x^3\right )+4\,{\ln \relax (2)}^2+4\,x^4-4\,x^5+x^6}\right )}^2+\left (4\,x^6+16\,\ln \relax (2)\,x^3\right )\,\ln \left (\frac {2\,\ln \relax (2)\,\left (110\,x^2-50\,x^3\right )+100\,{\ln \relax (2)}^2+121\,x^4-110\,x^5+25\,x^6}{2\,\ln \relax (2)\,\left (4\,x^2-2\,x^3\right )+4\,{\ln \relax (2)}^2+4\,x^4-4\,x^5+x^6}\right )}{2\,\ln \relax (2)\,\left (21\,x^2-10\,x^3\right )+20\,{\ln \relax (2)}^2+22\,x^4-21\,x^5+5\,x^6} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) +
4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))^2*(2*log(2)*(42*x^3 - 20*x^4) + 40*x*log(2)^2 + 44*x^5 - 42*x^6 + 10*x^7)
+ log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*
log(2)^2 + 4*x^4 - 4*x^5 + x^6))*(16*x^3*log(2) + 4*x^6))/(2*log(2)*(21*x^2 - 10*x^3) + 20*log(2)^2 + 22*x^4 -
21*x^5 + 5*x^6),x)
[Out]
int((log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) +
4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))^2*(2*log(2)*(42*x^3 - 20*x^4) + 40*x*log(2)^2 + 44*x^5 - 42*x^6 + 10*x^7)
+ log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*
log(2)^2 + 4*x^4 - 4*x^5 + x^6))*(16*x^3*log(2) + 4*x^6))/(2*log(2)*(21*x^2 - 10*x^3) + 20*log(2)^2 + 22*x^4 -
21*x^5 + 5*x^6), x)
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sympy [B] time = 0.36, size = 75, normalized size = 2.59 \begin {gather*} x^{2} \log {\left (\frac {25 x^{6} - 110 x^{5} + 121 x^{4} + \left (- 100 x^{3} + 220 x^{2}\right ) \log {\relax (2 )} + 100 \log {\relax (2 )}^{2}}{x^{6} - 4 x^{5} + 4 x^{4} + \left (- 4 x^{3} + 8 x^{2}\right ) \log {\relax (2 )} + 4 \log {\relax (2 )}^{2}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((40*x*ln(2)**2+2*(-20*x**4+42*x**3)*ln(2)+10*x**7-42*x**6+44*x**5)*ln((100*ln(2)**2+2*(-50*x**3+110
*x**2)*ln(2)+25*x**6-110*x**5+121*x**4)/(4*ln(2)**2+2*(-2*x**3+4*x**2)*ln(2)+x**6-4*x**5+4*x**4))**2+(16*x**3*
ln(2)+4*x**6)*ln((100*ln(2)**2+2*(-50*x**3+110*x**2)*ln(2)+25*x**6-110*x**5+121*x**4)/(4*ln(2)**2+2*(-2*x**3+4
*x**2)*ln(2)+x**6-4*x**5+4*x**4)))/(20*ln(2)**2+2*(-10*x**3+21*x**2)*ln(2)+5*x**6-21*x**5+22*x**4),x)
[Out]
x**2*log((25*x**6 - 110*x**5 + 121*x**4 + (-100*x**3 + 220*x**2)*log(2) + 100*log(2)**2)/(x**6 - 4*x**5 + 4*x*
*4 + (-4*x**3 + 8*x**2)*log(2) + 4*log(2)**2))**2
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