Optimal. Leaf size=24 \[ e^{x^3}+x+\left (-e^x+x\right ) \left (x-x^2+\log (25)\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 45, normalized size of antiderivative = 1.88, number of steps used = 10, number of rules used = 4, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2209, 2196, 2176, 2194} \begin {gather*} -x^3+e^{x^3}+e^x x^2+x^2-e^x x+e^x+x (1+\log (25))-e^x (1+\log (25)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 2196
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x^2-x^3+x (1+\log (25))+3 \int e^{x^3} x^2 \, dx+\int e^x \left (-1+x+x^2-\log (25)\right ) \, dx\\ &=e^{x^3}+x^2-x^3+x (1+\log (25))+\int \left (e^x x+e^x x^2+e^x (-1-\log (25))\right ) \, dx\\ &=e^{x^3}+x^2-x^3+x (1+\log (25))+(-1-\log (25)) \int e^x \, dx+\int e^x x \, dx+\int e^x x^2 \, dx\\ &=e^{x^3}+e^x x+x^2+e^x x^2-x^3-e^x (1+\log (25))+x (1+\log (25))-2 \int e^x x \, dx-\int e^x \, dx\\ &=-e^x+e^{x^3}-e^x x+x^2+e^x x^2-x^3-e^x (1+\log (25))+x (1+\log (25))+2 \int e^x \, dx\\ &=e^x+e^{x^3}-e^x x+x^2+e^x x^2-x^3-e^x (1+\log (25))+x (1+\log (25))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 34, normalized size = 1.42 \begin {gather*} e^{x^3}+x+x^2-x^3+e^x \left (-x+x^2-\log (25)\right )+x \log (25) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 33, normalized size = 1.38 \begin {gather*} -x^{3} + x^{2} + {\left (x^{2} - x - 2 \, \log \relax (5)\right )} e^{x} + 2 \, x \log \relax (5) + x + e^{\left (x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 33, normalized size = 1.38 \begin {gather*} -x^{3} + x^{2} + {\left (x^{2} - x - 2 \, \log \relax (5)\right )} e^{x} + 2 \, x \log \relax (5) + x + e^{\left (x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 34, normalized size = 1.42
method | result | size |
risch | \({\mathrm e}^{x^{3}}+\left (x^{2}-2 \ln \relax (5)-x \right ) {\mathrm e}^{x}+2 x \ln \relax (5)-x^{3}+x^{2}+x\) | \(34\) |
default | \(x -{\mathrm e}^{x} x +{\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} \ln \relax (5)+x^{2}-x^{3}+{\mathrm e}^{x^{3}}+2 x \ln \relax (5)\) | \(37\) |
norman | \(x^{2}+\left (2 \ln \relax (5)+1\right ) x +{\mathrm e}^{x} x^{2}-x^{3}-{\mathrm e}^{x} x -2 \,{\mathrm e}^{x} \ln \relax (5)+{\mathrm e}^{x^{3}}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 33, normalized size = 1.38 \begin {gather*} -x^{3} + x^{2} + {\left (x^{2} - x - 2 \, \log \relax (5)\right )} e^{x} + 2 \, x \log \relax (5) + x + e^{\left (x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.23, size = 36, normalized size = 1.50 \begin {gather*} {\mathrm {e}}^{x^3}+x^2\,{\mathrm {e}}^x+x\,\left (\ln \left (25\right )+1\right )-{\mathrm {e}}^x\,\ln \left (25\right )-x\,{\mathrm {e}}^x+x^2-x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 32, normalized size = 1.33 \begin {gather*} - x^{3} + x^{2} + x \left (1 + 2 \log {\relax (5 )}\right ) + \left (x^{2} - x - 2 \log {\relax (5 )}\right ) e^{x} + e^{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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