Optimal. Leaf size=19 \[ \left (7+e^{4/3}+22 x+e^x x \log (5)\right )^2 \]
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Rubi [B] time = 0.15, antiderivative size = 72, normalized size of antiderivative = 3.79, number of steps used = 19, number of rules used = 4, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2196, 2194, 2176, 1593} \begin {gather*} 484 x^2+e^{2 x} x^2 \log ^2(5)+44 e^x x^2 \log (5)+44 \left (7+e^{4/3}\right ) x+14 e^x x \log (5)-2 e^{x+\frac {4}{3}} \log (5)+2 e^{x+\frac {4}{3}} (x+1) \log (5) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=44 \left (7+e^{4/3}\right ) x+484 x^2+\log (5) \int e^x \left (14+102 x+44 x^2+e^{4/3} (2+2 x)\right ) \, dx+\log ^2(5) \int e^{2 x} \left (2 x+2 x^2\right ) \, dx\\ &=44 \left (7+e^{4/3}\right ) x+484 x^2+\log (5) \int \left (14 e^x+102 e^x x+44 e^x x^2+2 e^{\frac {4}{3}+x} (1+x)\right ) \, dx+\log ^2(5) \int e^{2 x} x (2+2 x) \, dx\\ &=44 \left (7+e^{4/3}\right ) x+484 x^2+(2 \log (5)) \int e^{\frac {4}{3}+x} (1+x) \, dx+(14 \log (5)) \int e^x \, dx+(44 \log (5)) \int e^x x^2 \, dx+(102 \log (5)) \int e^x x \, dx+\log ^2(5) \int \left (2 e^{2 x} x+2 e^{2 x} x^2\right ) \, dx\\ &=44 \left (7+e^{4/3}\right ) x+484 x^2+14 e^x \log (5)+102 e^x x \log (5)+44 e^x x^2 \log (5)+2 e^{\frac {4}{3}+x} (1+x) \log (5)-(2 \log (5)) \int e^{\frac {4}{3}+x} \, dx-(88 \log (5)) \int e^x x \, dx-(102 \log (5)) \int e^x \, dx+\left (2 \log ^2(5)\right ) \int e^{2 x} x \, dx+\left (2 \log ^2(5)\right ) \int e^{2 x} x^2 \, dx\\ &=44 \left (7+e^{4/3}\right ) x+484 x^2-88 e^x \log (5)-2 e^{\frac {4}{3}+x} \log (5)+14 e^x x \log (5)+44 e^x x^2 \log (5)+2 e^{\frac {4}{3}+x} (1+x) \log (5)+e^{2 x} x \log ^2(5)+e^{2 x} x^2 \log ^2(5)+(88 \log (5)) \int e^x \, dx-\log ^2(5) \int e^{2 x} \, dx-\left (2 \log ^2(5)\right ) \int e^{2 x} x \, dx\\ &=44 \left (7+e^{4/3}\right ) x+484 x^2-2 e^{\frac {4}{3}+x} \log (5)+14 e^x x \log (5)+44 e^x x^2 \log (5)+2 e^{\frac {4}{3}+x} (1+x) \log (5)-\frac {1}{2} e^{2 x} \log ^2(5)+e^{2 x} x^2 \log ^2(5)+\log ^2(5) \int e^{2 x} \, dx\\ &=44 \left (7+e^{4/3}\right ) x+484 x^2-2 e^{\frac {4}{3}+x} \log (5)+14 e^x x \log (5)+44 e^x x^2 \log (5)+2 e^{\frac {4}{3}+x} (1+x) \log (5)+e^{2 x} x^2 \log ^2(5)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 29, normalized size = 1.53 \begin {gather*} x \left (22+e^x \log (5)\right ) \left (14+2 e^{4/3}+22 x+e^x x \log (5)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.63, size = 45, normalized size = 2.37 \begin {gather*} x^{2} e^{\left (2 \, x\right )} \log \relax (5)^{2} + 2 \, {\left (22 \, x^{2} + x e^{\frac {4}{3}} + 7 \, x\right )} e^{x} \log \relax (5) + 484 \, x^{2} + 44 \, x e^{\frac {4}{3}} + 308 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.35, size = 49, normalized size = 2.58 \begin {gather*} x^{2} e^{\left (2 \, x\right )} \log \relax (5)^{2} + 484 \, x^{2} + 44 \, x e^{\frac {4}{3}} + 2 \, {\left (x e^{\left (x + \frac {4}{3}\right )} + {\left (22 \, x^{2} + 7 \, x\right )} e^{x}\right )} \log \relax (5) + 308 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.03, size = 46, normalized size = 2.42
method | result | size |
risch | \({\mathrm e}^{2 x} \ln \relax (5)^{2} x^{2}+\ln \relax (5) \left (2 x \,{\mathrm e}^{\frac {4}{3}}+44 x^{2}+14 x \right ) {\mathrm e}^{x}+44 x \,{\mathrm e}^{\frac {4}{3}}+484 x^{2}+308 x\) | \(46\) |
norman | \(\left (44 \,{\mathrm e}^{\frac {4}{3}}+308\right ) x +\left (2 \ln \relax (5) {\mathrm e}^{\frac {4}{3}}+14 \ln \relax (5)\right ) x \,{\mathrm e}^{x}+{\mathrm e}^{2 x} \ln \relax (5)^{2} x^{2}+484 x^{2}+44 x^{2} \ln \relax (5) {\mathrm e}^{x}\) | \(51\) |
default | \(308 x +2 \,{\mathrm e}^{x} \ln \relax (5) {\mathrm e}^{\frac {4}{3}} x +44 x^{2} \ln \relax (5) {\mathrm e}^{x}+14 x \,{\mathrm e}^{x} \ln \relax (5)+{\mathrm e}^{2 x} \ln \relax (5)^{2} x^{2}+484 x^{2}+44 x \,{\mathrm e}^{\frac {4}{3}}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.51, size = 44, normalized size = 2.32 \begin {gather*} x^{2} e^{\left (2 \, x\right )} \log \relax (5)^{2} + 2 \, {\left (22 \, x^{2} + x {\left (e^{\frac {4}{3}} + 7\right )}\right )} e^{x} \log \relax (5) + 484 \, x^{2} + 44 \, x e^{\frac {4}{3}} + 308 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.29, size = 24, normalized size = 1.26 \begin {gather*} x\,\left ({\mathrm {e}}^x\,\ln \relax (5)+22\right )\,\left (22\,x+2\,{\mathrm {e}}^{4/3}+x\,{\mathrm {e}}^x\,\ln \relax (5)+14\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 58, normalized size = 3.05 \begin {gather*} x^{2} e^{2 x} \log {\relax (5 )}^{2} + 484 x^{2} + x \left (44 e^{\frac {4}{3}} + 308\right ) + \left (44 x^{2} \log {\relax (5 )} + 2 x e^{\frac {4}{3}} \log {\relax (5 )} + 14 x \log {\relax (5 )}\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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