Optimal. Leaf size=24 \[ -3 x^3+x^2 \log ^2(x)-e^x \log (1+\log (4)) \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {2304, 2305, 2194} \begin {gather*} -3 x^3+x^2 \log ^2(x)-e^x \log (1+\log (4)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-3 x^3+2 \int x \log (x) \, dx+2 \int x \log ^2(x) \, dx-\log (1+\log (4)) \int e^x \, dx\\ &=-\frac {x^2}{2}-3 x^3+x^2 \log (x)+x^2 \log ^2(x)-e^x \log (1+\log (4))-2 \int x \log (x) \, dx\\ &=-3 x^3+x^2 \log ^2(x)-e^x \log (1+\log (4))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.00 \begin {gather*} -3 x^3+x^2 \log ^2(x)-e^x \log (1+\log (4)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.14, size = 25, normalized size = 1.04 \begin {gather*} x^{2} \log \relax (x)^{2} - 3 \, x^{3} - e^{x} \log \left (2 \, \log \relax (2) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 25, normalized size = 1.04 \begin {gather*} x^{2} \log \relax (x)^{2} - 3 \, x^{3} - e^{x} \log \left (2 \, \log \relax (2) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 26, normalized size = 1.08
method | result | size |
default | \(x^{2} \ln \relax (x )^{2}-{\mathrm e}^{x} \ln \left (1+2 \ln \relax (2)\right )-3 x^{3}\) | \(26\) |
norman | \(x^{2} \ln \relax (x )^{2}-{\mathrm e}^{x} \ln \left (1+2 \ln \relax (2)\right )-3 x^{3}\) | \(26\) |
risch | \(x^{2} \ln \relax (x )^{2}-{\mathrm e}^{x} \ln \left (1+2 \ln \relax (2)\right )-3 x^{3}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 45, normalized size = 1.88 \begin {gather*} \frac {1}{2} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} - 3 \, x^{3} + x^{2} \log \relax (x) - \frac {1}{2} \, x^{2} - e^{x} \log \left (2 \, \log \relax (2) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.32, size = 25, normalized size = 1.04 \begin {gather*} x^2\,{\ln \relax (x)}^2-{\mathrm {e}}^x\,\ln \left (2\,\ln \relax (2)+1\right )-3\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 24, normalized size = 1.00 \begin {gather*} - 3 x^{3} + x^{2} \log {\relax (x )}^{2} - e^{x} \log {\left (1 + 2 \log {\relax (2 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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