Optimal. Leaf size=22 \[ 2 e^{x-(3+x)^x} (1-2 x)-3 x \]
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Rubi [F] time = 2.45, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {9-15 x-6 x^2+e^{x-(3+x)^x} (1-2 x) \left (6+14 x+4 x^2+(3+x)^x \left (2 x-4 x^2+\left (6-10 x-4 x^2\right ) \log (3+x)\right )\right )}{-3+5 x+2 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {6 e^{x-(3+x)^x}}{3+x}-\frac {14 e^{x-(3+x)^x} x}{3+x}-\frac {4 e^{x-(3+x)^x} x^2}{3+x}+\frac {9}{(3+x) (-1+2 x)}-\frac {15 x}{-3+5 x+2 x^2}-\frac {6 x^2}{-3+5 x+2 x^2}+2 e^{x-(3+x)^x} (3+x)^{-1+x} (-1+2 x) (x+3 \log (3+x)+x \log (3+x))\right ) \, dx\\ &=2 \int e^{x-(3+x)^x} (3+x)^{-1+x} (-1+2 x) (x+3 \log (3+x)+x \log (3+x)) \, dx-4 \int \frac {e^{x-(3+x)^x} x^2}{3+x} \, dx-6 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx-6 \int \frac {x^2}{-3+5 x+2 x^2} \, dx+9 \int \frac {1}{(3+x) (-1+2 x)} \, dx-14 \int \frac {e^{x-(3+x)^x} x}{3+x} \, dx-15 \int \frac {x}{-3+5 x+2 x^2} \, dx\\ &=-3 x-\frac {9}{7} \int \frac {1}{3+x} \, dx+2 \int \left (e^{x-(3+x)^x} x (3+x)^{-1+x} (-1+2 x)+e^{x-(3+x)^x} (3+x)^{-1+x} \left (-3+5 x+2 x^2\right ) \log (3+x)\right ) \, dx-\frac {15}{7} \int \frac {1}{-1+2 x} \, dx+\frac {18}{7} \int \frac {1}{-1+2 x} \, dx-3 \int \frac {3-5 x}{-3+5 x+2 x^2} \, dx-4 \int \left (-3 e^{x-(3+x)^x}+e^{x-(3+x)^x} x+\frac {9 e^{x-(3+x)^x}}{3+x}\right ) \, dx-6 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx-\frac {90}{7} \int \frac {1}{6+2 x} \, dx-14 \int \left (e^{x-(3+x)^x}-\frac {3 e^{x-(3+x)^x}}{3+x}\right ) \, dx\\ &=-3 x+\frac {3}{14} \log (1-2 x)-\frac {54}{7} \log (3+x)-\frac {3}{7} \int \frac {1}{-1+2 x} \, dx+2 \int e^{x-(3+x)^x} x (3+x)^{-1+x} (-1+2 x) \, dx+2 \int e^{x-(3+x)^x} (3+x)^{-1+x} \left (-3+5 x+2 x^2\right ) \log (3+x) \, dx-4 \int e^{x-(3+x)^x} x \, dx-6 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+12 \int e^{x-(3+x)^x} \, dx-14 \int e^{x-(3+x)^x} \, dx+\frac {108}{7} \int \frac {1}{6+2 x} \, dx-36 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+42 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx\\ &=-3 x+2 \int \left (-e^{x-(3+x)^x} x (3+x)^{-1+x}+2 e^{x-(3+x)^x} x^2 (3+x)^{-1+x}\right ) \, dx-2 \int \frac {-\int e^{x-(3+x)^x} (3+x)^x \, dx+2 \int e^{x-(3+x)^x} x (3+x)^x \, dx}{3+x} \, dx-4 \int e^{x-(3+x)^x} x \, dx-6 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+12 \int e^{x-(3+x)^x} \, dx-14 \int e^{x-(3+x)^x} \, dx-36 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+42 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx-(2 \log (3+x)) \int e^{x-(3+x)^x} (3+x)^x \, dx+(4 \log (3+x)) \int e^{x-(3+x)^x} x (3+x)^x \, dx\\ &=-3 x-2 \int e^{x-(3+x)^x} x (3+x)^{-1+x} \, dx-2 \int \left (-\frac {\int e^{x-(3+x)^x} (3+x)^x \, dx}{3+x}+\frac {2 \int e^{x-(3+x)^x} x (3+x)^x \, dx}{3+x}\right ) \, dx-4 \int e^{x-(3+x)^x} x \, dx+4 \int e^{x-(3+x)^x} x^2 (3+x)^{-1+x} \, dx-6 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+12 \int e^{x-(3+x)^x} \, dx-14 \int e^{x-(3+x)^x} \, dx-36 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+42 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx-(2 \log (3+x)) \int e^{x-(3+x)^x} (3+x)^x \, dx+(4 \log (3+x)) \int e^{x-(3+x)^x} x (3+x)^x \, dx\\ &=-3 x-2 \int e^{x-(3+x)^x} x (3+x)^{-1+x} \, dx+2 \int \frac {\int e^{x-(3+x)^x} (3+x)^x \, dx}{3+x} \, dx-4 \int e^{x-(3+x)^x} x \, dx+4 \int e^{x-(3+x)^x} x^2 (3+x)^{-1+x} \, dx-4 \int \frac {\int e^{x-(3+x)^x} x (3+x)^x \, dx}{3+x} \, dx-6 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+12 \int e^{x-(3+x)^x} \, dx-14 \int e^{x-(3+x)^x} \, dx-36 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx+42 \int \frac {e^{x-(3+x)^x}}{3+x} \, dx-(2 \log (3+x)) \int e^{x-(3+x)^x} (3+x)^x \, dx+(4 \log (3+x)) \int e^{x-(3+x)^x} x (3+x)^x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 180.04, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.94, size = 22, normalized size = 1.00 \begin {gather*} -3 \, x + 2 \, e^{\left (-{\left (x + 3\right )}^{x} + x + \log \left (-2 \, x + 1\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {6 \, x^{2} + 2 \, {\left ({\left (2 \, x^{2} + {\left (2 \, x^{2} + 5 \, x - 3\right )} \log \left (x + 3\right ) - x\right )} {\left (x + 3\right )}^{x} - 2 \, x^{2} - 7 \, x - 3\right )} e^{\left (-{\left (x + 3\right )}^{x} + x + \log \left (-2 \, x + 1\right )\right )} + 15 \, x - 9}{2 \, x^{2} + 5 \, x - 3}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 22, normalized size = 1.00
method | result | size |
risch | \(2 \left (1-2 x \right ) {\mathrm e}^{-\left (3+x \right )^{x}+x}-3 x\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.76, size = 21, normalized size = 0.95 \begin {gather*} -2 \, {\left (2 \, x - 1\right )} e^{\left (-{\left (x + 3\right )}^{x} + x\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.27, size = 29, normalized size = 1.32 \begin {gather*} 2\,{\mathrm {e}}^{-{\left (x+3\right )}^x}\,{\mathrm {e}}^x-3\,x-4\,x\,{\mathrm {e}}^{-{\left (x+3\right )}^x}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 7.94, size = 19, normalized size = 0.86 \begin {gather*} - 3 x + \left (2 - 4 x\right ) e^{x - e^{x \log {\left (x + 3 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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