Optimal. Leaf size=25 \[ e^4 \left (3+x^2\right ) (1-x-\log (x)) (-3-x+\log (x)) \]
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Rubi [B] time = 0.32, antiderivative size = 60, normalized size of antiderivative = 2.40, number of steps used = 9, number of rules used = 7, integrand size = 88, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 6688, 14, 2351, 2301, 2304, 2305} \begin {gather*} e^4 x^4+2 e^4 x^3-e^4 x^2 \log ^2(x)+4 e^4 x^2 \log (x)+6 e^4 x-3 e^4 \log ^2(x)+12 e^4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2301
Rule 2304
Rule 2305
Rule 2351
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^4 \int \frac {\left (-3+2 x+x^2+4 \log (x)-\log ^2(x)\right ) \left (-12-6 x-4 x^2-6 x^3-4 x^4+\left (6-6 x^2\right ) \log (x)+2 x^2 \log ^2(x)\right )}{3 x-2 x^2-x^3-4 x \log (x)+x \log ^2(x)} \, dx\\ &=e^4 \int \left (6+\frac {12}{x}+4 x+6 x^2+4 x^3+\frac {6 \left (-1+x^2\right ) \log (x)}{x}-2 x \log ^2(x)\right ) \, dx\\ &=6 e^4 x+2 e^4 x^2+2 e^4 x^3+e^4 x^4+12 e^4 \log (x)-\left (2 e^4\right ) \int x \log ^2(x) \, dx+\left (6 e^4\right ) \int \frac {\left (-1+x^2\right ) \log (x)}{x} \, dx\\ &=6 e^4 x+2 e^4 x^2+2 e^4 x^3+e^4 x^4+12 e^4 \log (x)-e^4 x^2 \log ^2(x)+\left (2 e^4\right ) \int x \log (x) \, dx+\left (6 e^4\right ) \int \left (-\frac {\log (x)}{x}+x \log (x)\right ) \, dx\\ &=6 e^4 x+\frac {3 e^4 x^2}{2}+2 e^4 x^3+e^4 x^4+12 e^4 \log (x)+e^4 x^2 \log (x)-e^4 x^2 \log ^2(x)-\left (6 e^4\right ) \int \frac {\log (x)}{x} \, dx+\left (6 e^4\right ) \int x \log (x) \, dx\\ &=6 e^4 x+2 e^4 x^3+e^4 x^4+12 e^4 \log (x)+4 e^4 x^2 \log (x)-3 e^4 \log ^2(x)-e^4 x^2 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 60, normalized size = 2.40 \begin {gather*} 6 e^4 x+2 e^4 x^3+e^4 x^4+12 e^4 \log (x)+4 e^4 x^2 \log (x)-3 e^4 \log ^2(x)-e^4 x^2 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 40, normalized size = 1.60 \begin {gather*} -{\left (x^{2} + 3\right )} e^{4} \log \relax (x)^{2} + 4 \, {\left (x^{2} + 3\right )} e^{4} \log \relax (x) + {\left (x^{4} + 2 \, x^{3} + 6 \, x\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 53, normalized size = 2.12 \begin {gather*} x^{4} e^{4} - x^{2} e^{4} \log \relax (x)^{2} + 2 \, x^{3} e^{4} + 4 \, x^{2} e^{4} \log \relax (x) - 3 \, e^{4} \log \relax (x)^{2} + 6 \, x e^{4} + 12 \, e^{4} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 42, normalized size = 1.68
method | result | size |
default | \({\mathrm e}^{4} \left (-x^{2} \ln \relax (x )^{2}+4 x^{2} \ln \relax (x )+x^{4}+2 x^{3}-3 \ln \relax (x )^{2}+6 x +12 \ln \relax (x )\right )\) | \(42\) |
risch | \({\mathrm e}^{4} \left (-x^{2}-3\right ) \ln \relax (x )^{2}+4 x^{2} {\mathrm e}^{4} \ln \relax (x )+x^{4} {\mathrm e}^{4}+2 x^{3} {\mathrm e}^{4}+6 x \,{\mathrm e}^{4}+12 \,{\mathrm e}^{4} \ln \relax (x )\) | \(49\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 35, normalized size = 1.40 \begin {gather*} {\left (x^{4} + 2 \, x^{3} - {\left (x^{2} + 3\right )} \log \relax (x)^{2} + 4 \, {\left (x^{2} + 3\right )} \log \relax (x) + 6 \, x\right )} e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.10, size = 41, normalized size = 1.64 \begin {gather*} {\mathrm {e}}^4\,\left (x^4+2\,x^3-x^2\,{\ln \relax (x)}^2+4\,x^2\,\ln \relax (x)+6\,x-3\,{\ln \relax (x)}^2+12\,\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.31, size = 60, normalized size = 2.40 \begin {gather*} x^{4} e^{4} + 2 x^{3} e^{4} + 4 x^{2} e^{4} \log {\relax (x )} + 6 x e^{4} + \left (- x^{2} e^{4} - 3 e^{4}\right ) \log {\relax (x )}^{2} + 12 e^{4} \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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