Optimal. Leaf size=36 \[ \left (\frac {3}{x}+x^2\right ) \left (6-e^x-x-\left (-5+\frac {x-\log (2)}{x}\right )^2\right ) \]
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Rubi [A] time = 0.14, antiderivative size = 53, normalized size of antiderivative = 1.47, number of steps used = 14, number of rules used = 6, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {14, 2199, 2177, 2178, 2176, 2194} \begin {gather*} -x^3-\frac {3 \log ^2(2)}{x^3}-e^x x^2-10 x^2-\frac {24 \log (2)}{x^2}-\frac {3 e^x}{x}-\frac {30}{x}-8 x \log (2) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2176
Rule 2177
Rule 2178
Rule 2194
Rule 2199
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {e^x \left (-3+3 x+2 x^3+x^4\right )}{x^2}+\frac {30 x^2-20 x^5-3 x^6+48 x \log (2)-8 x^4 \log (2)+9 \log ^2(2)}{x^4}\right ) \, dx\\ &=-\int \frac {e^x \left (-3+3 x+2 x^3+x^4\right )}{x^2} \, dx+\int \frac {30 x^2-20 x^5-3 x^6+48 x \log (2)-8 x^4 \log (2)+9 \log ^2(2)}{x^4} \, dx\\ &=-\int \left (-\frac {3 e^x}{x^2}+\frac {3 e^x}{x}+2 e^x x+e^x x^2\right ) \, dx+\int \left (\frac {30}{x^2}-20 x-3 x^2-8 \log (2)+\frac {48 \log (2)}{x^3}+\frac {9 \log ^2(2)}{x^4}\right ) \, dx\\ &=-\frac {30}{x}-10 x^2-x^3-\frac {24 \log (2)}{x^2}-8 x \log (2)-\frac {3 \log ^2(2)}{x^3}-2 \int e^x x \, dx+3 \int \frac {e^x}{x^2} \, dx-3 \int \frac {e^x}{x} \, dx-\int e^x x^2 \, dx\\ &=-\frac {30}{x}-\frac {3 e^x}{x}-2 e^x x-10 x^2-e^x x^2-x^3-3 \text {Ei}(x)-\frac {24 \log (2)}{x^2}-8 x \log (2)-\frac {3 \log ^2(2)}{x^3}+2 \int e^x \, dx+2 \int e^x x \, dx+3 \int \frac {e^x}{x} \, dx\\ &=2 e^x-\frac {30}{x}-\frac {3 e^x}{x}-10 x^2-e^x x^2-x^3-\frac {24 \log (2)}{x^2}-8 x \log (2)-\frac {3 \log ^2(2)}{x^3}-2 \int e^x \, dx\\ &=-\frac {30}{x}-\frac {3 e^x}{x}-10 x^2-e^x x^2-x^3-\frac {24 \log (2)}{x^2}-8 x \log (2)-\frac {3 \log ^2(2)}{x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 46, normalized size = 1.28 \begin {gather*} -\frac {3 \left (10+e^x\right ) x^2+\left (10+e^x\right ) x^5+x^6+24 x \log (2)+8 x^4 \log (2)+3 \log ^2(2)}{x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 48, normalized size = 1.33 \begin {gather*} -\frac {x^{6} + 10 \, x^{5} + 30 \, x^{2} + {\left (x^{5} + 3 \, x^{2}\right )} e^{x} + 8 \, {\left (x^{4} + 3 \, x\right )} \log \relax (2) + 3 \, \log \relax (2)^{2}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 50, normalized size = 1.39 \begin {gather*} -\frac {x^{6} + x^{5} e^{x} + 10 \, x^{5} + 8 \, x^{4} \log \relax (2) + 3 \, x^{2} e^{x} + 30 \, x^{2} + 24 \, x \log \relax (2) + 3 \, \log \relax (2)^{2}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 50, normalized size = 1.39
method | result | size |
risch | \(-x^{3}-8 x \ln \relax (2)-10 x^{2}+\frac {-3 \ln \relax (2)^{2}-24 x \ln \relax (2)-30 x^{2}}{x^{3}}-\frac {\left (x^{3}+3\right ) {\mathrm e}^{x}}{x}\) | \(50\) |
default | \(-10 x^{2}-\frac {30}{x}-x^{3}-\frac {24 \ln \relax (2)}{x^{2}}-\frac {3 \,{\mathrm e}^{x}}{x}-{\mathrm e}^{x} x^{2}-\frac {3 \ln \relax (2)^{2}}{x^{3}}-8 x \ln \relax (2)\) | \(52\) |
norman | \(\frac {-30 x^{2}-10 x^{5}-x^{6}-3 \ln \relax (2)^{2}-24 x \ln \relax (2)-8 x^{4} \ln \relax (2)-x^{5} {\mathrm e}^{x}-3 \,{\mathrm e}^{x} x^{2}}{x^{3}}\) | \(53\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.39, size = 67, normalized size = 1.86 \begin {gather*} -x^{3} - 10 \, x^{2} - {\left (x^{2} - 2 \, x + 2\right )} e^{x} - 2 \, {\left (x - 1\right )} e^{x} - 8 \, x \log \relax (2) - \frac {30}{x} - \frac {24 \, \log \relax (2)}{x^{2}} - \frac {3 \, \log \relax (2)^{2}}{x^{3}} - 3 \, {\rm Ei}\relax (x) + 3 \, \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 47, normalized size = 1.31 \begin {gather*} -x\,\ln \left (256\right )-x^2\,\left ({\mathrm {e}}^x+10\right )-x^3-\frac {24\,x\,\ln \relax (2)+3\,{\ln \relax (2)}^2+x^2\,\left (3\,{\mathrm {e}}^x+30\right )}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.23, size = 48, normalized size = 1.33 \begin {gather*} - x^{3} - 10 x^{2} - 8 x \log {\relax (2 )} + \frac {\left (- x^{3} - 3\right ) e^{x}}{x} - \frac {30 x^{2} + 24 x \log {\relax (2 )} + 3 \log {\relax (2 )}^{2}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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