Optimal. Leaf size=23 \[ 2-x^2-x \left (1+e^3 x^2+\log (x)\right )^2 \]
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Rubi [B] time = 0.03, antiderivative size = 52, normalized size of antiderivative = 2.26, number of steps used = 6, number of rules used = 4, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2313, 12, 2296, 2295} \begin {gather*} -e^6 x^5-2 e^3 x^3-2 \left (e^3 x^3+2 x\right ) \log (x)-x^2-x-x \log ^2(x)+2 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2295
Rule 2296
Rule 2313
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-3 x-x^2-\frac {8 e^3 x^3}{3}-e^6 x^5+\int \left (-4-6 e^3 x^2\right ) \log (x) \, dx-\int \log ^2(x) \, dx\\ &=-3 x-x^2-\frac {8 e^3 x^3}{3}-e^6 x^5-2 \left (2 x+e^3 x^3\right ) \log (x)-x \log ^2(x)+2 \int \log (x) \, dx-\int 2 \left (-2-e^3 x^2\right ) \, dx\\ &=-5 x-x^2-\frac {8 e^3 x^3}{3}-e^6 x^5+2 x \log (x)-2 \left (2 x+e^3 x^3\right ) \log (x)-x \log ^2(x)-2 \int \left (-2-e^3 x^2\right ) \, dx\\ &=-x-x^2-2 e^3 x^3-e^6 x^5+2 x \log (x)-2 \left (2 x+e^3 x^3\right ) \log (x)-x \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 47, normalized size = 2.04 \begin {gather*} -x-x^2-2 e^3 x^3-e^6 x^5-2 x \log (x)-2 e^3 x^3 \log (x)-x \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 42, normalized size = 1.83 \begin {gather*} -x^{5} e^{6} - 2 \, x^{3} e^{3} - x \log \relax (x)^{2} - x^{2} - 2 \, {\left (x^{3} e^{3} + x\right )} \log \relax (x) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 44, normalized size = 1.91 \begin {gather*} -x^{5} e^{6} - 2 \, x^{3} e^{3} \log \relax (x) - 2 \, x^{3} e^{3} - x \log \relax (x)^{2} - x^{2} - 2 \, x \log \relax (x) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 45, normalized size = 1.96
method | result | size |
risch | \(-x -2 \,{\mathrm e}^{3} \ln \relax (x ) x^{3}-2 x^{3} {\mathrm e}^{3}-2 x \ln \relax (x )-x^{2}-x \ln \relax (x )^{2}-x^{5} {\mathrm e}^{6}\) | \(45\) |
default | \(-x -2 \,{\mathrm e}^{3} \ln \relax (x ) x^{3}-2 x^{3} {\mathrm e}^{3}-2 x \ln \relax (x )-x^{2}-x \ln \relax (x )^{2}-x^{5} {\mathrm e}^{6}\) | \(47\) |
norman | \(-x -2 \,{\mathrm e}^{3} \ln \relax (x ) x^{3}-2 x^{3} {\mathrm e}^{3}-2 x \ln \relax (x )-x^{2}-x \ln \relax (x )^{2}-x^{5} {\mathrm e}^{6}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 48, normalized size = 2.09 \begin {gather*} -x^{5} e^{6} - 2 \, x^{3} e^{3} - {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x - x^{2} - 2 \, {\left (x^{3} e^{3} + 2 \, x\right )} \log \relax (x) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.11, size = 36, normalized size = 1.57 \begin {gather*} -x\,\left ({\mathrm {e}}^6\,x^4+2\,{\mathrm {e}}^3\,x^2\,\ln \relax (x)+2\,{\mathrm {e}}^3\,x^2+x+{\ln \relax (x)}^2+2\,\ln \relax (x)+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.13, size = 42, normalized size = 1.83 \begin {gather*} - x^{5} e^{6} - 2 x^{3} e^{3} - x^{2} - x \log {\relax (x )}^{2} - x + \left (- 2 x^{3} e^{3} - 2 x\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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