Optimal. Leaf size=26 \[ 5 \left (3 e^{-5+x}+x \log \left (-3+x \left (-e^4+x^2\right )\right )\right ) \]
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Rubi [A] time = 10.55, antiderivative size = 23, normalized size of antiderivative = 0.88, number of steps used = 24, number of rules used = 10, integrand size = 72, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.139, Rules used = {6742, 2194, 6688, 2079, 800, 634, 618, 206, 628, 2523} \begin {gather*} 5 x \log \left (x^3-e^4 x-3\right )+15 e^{x-5} \end {gather*}
Antiderivative was successfully verified.
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Rule 206
Rule 618
Rule 628
Rule 634
Rule 800
Rule 2079
Rule 2194
Rule 2523
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (15 e^{-5+x}+\frac {5 \left (-e^4 x+3 x^3-3 \log \left (-3-e^4 x+x^3\right )-e^4 x \log \left (-3-e^4 x+x^3\right )+x^3 \log \left (-3-e^4 x+x^3\right )\right )}{-3-e^4 x+x^3}\right ) \, dx\\ &=5 \int \frac {-e^4 x+3 x^3-3 \log \left (-3-e^4 x+x^3\right )-e^4 x \log \left (-3-e^4 x+x^3\right )+x^3 \log \left (-3-e^4 x+x^3\right )}{-3-e^4 x+x^3} \, dx+15 \int e^{-5+x} \, dx\\ &=15 e^{-5+x}+5 \int \left (\frac {x \left (e^4-3 x^2\right )}{3+e^4 x-x^3}+\log \left (-3-e^4 x+x^3\right )\right ) \, dx\\ &=15 e^{-5+x}+5 \int \frac {x \left (e^4-3 x^2\right )}{3+e^4 x-x^3} \, dx+5 \int \log \left (-3-e^4 x+x^3\right ) \, dx\\ &=15 e^{-5+x}+5 x \log \left (-3-e^4 x+x^3\right )-5 \int \frac {x \left (-e^4+3 x^2\right )}{-3-e^4 x+x^3} \, dx+5 \int \left (3-\frac {9+2 e^4 x}{3+e^4 x-x^3}\right ) \, dx\\ &=15 e^{-5+x}+15 x+5 x \log \left (-3-e^4 x+x^3\right )-5 \int \frac {9+2 e^4 x}{3+e^4 x-x^3} \, dx-5 \int \left (3+\frac {9+2 e^4 x}{-3-e^4 x+x^3}\right ) \, dx\\ &=15 e^{-5+x}+5 x \log \left (-3-e^4 x+x^3\right )-5 \int \frac {9+2 e^4 x}{\left (\frac {1}{3} \left (\frac {3^{2/3} e^4}{\sqrt [3]{\frac {1}{2} \left (27+i \sqrt {-729+12 e^{12}}\right )}}+\sqrt [3]{\frac {3}{2} \left (27+i \sqrt {-729+12 e^{12}}\right )}\right )-x\right ) \left (\frac {1}{18} \left (-6 e^4+\frac {6 \sqrt [3]{3} e^8}{\left (\frac {1}{2} \left (27+i \sqrt {-729+12 e^{12}}\right )\right )^{2/3}}+\sqrt [3]{2} \left (3 \left (27+i \sqrt {-729+12 e^{12}}\right )\right )^{2/3}\right )+\frac {1}{3} \left (\frac {3^{2/3} e^4}{\sqrt [3]{\frac {1}{2} \left (27+i \sqrt {-729+12 e^{12}}\right )}}+\sqrt [3]{\frac {3}{2} \left (27+i \sqrt {-729+12 e^{12}}\right )}\right ) x+x^2\right )} \, dx-5 \int \frac {9+2 e^4 x}{-3-e^4 x+x^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 24, normalized size = 0.92 \begin {gather*} 5 \left (3 e^{-5+x}+x \log \left (-3-e^4 x+x^3\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 21, normalized size = 0.81 \begin {gather*} 5 \, x \log \left (x^{3} - x e^{4} - 3\right ) + 15 \, e^{\left (x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 24, normalized size = 0.92 \begin {gather*} 5 \, {\left (x e^{5} \log \left (x^{3} - x e^{4} - 3\right ) + 3 \, e^{x}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 22, normalized size = 0.85
method | result | size |
default | \(15 \,{\mathrm e}^{x -5}+5 x \ln \left (-x \,{\mathrm e}^{4}+x^{3}-3\right )\) | \(22\) |
norman | \(15 \,{\mathrm e}^{x -5}+5 x \ln \left (-x \,{\mathrm e}^{4}+x^{3}-3\right )\) | \(22\) |
risch | \(15 \,{\mathrm e}^{x -5}+5 x \ln \left (-x \,{\mathrm e}^{4}+x^{3}-3\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 24, normalized size = 0.92 \begin {gather*} 5 \, {\left (x e^{5} \log \left (x^{3} - x e^{4} - 3\right ) + 3 \, e^{x}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.15, size = 21, normalized size = 0.81 \begin {gather*} 15\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^x+5\,x\,\ln \left (x^3-{\mathrm {e}}^4\,x-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.70, size = 20, normalized size = 0.77 \begin {gather*} 5 x \log {\left (x^{3} - x e^{4} - 3 \right )} + 15 e^{x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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