Optimal. Leaf size=36 \[ -2+\frac {17 x}{16}+\frac {e^{\frac {x}{2-x}}}{-e^{(-1+x) x^2}+x^2} \]
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Rubi [F]
time = 10.64, 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 {68 x^4-68 x^5+17 x^6+e^{-2 x^2+2 x^3} \left (68-68 x+17 x^2\right )+e^{-\frac {x}{-2+x}} \left (-128 x+160 x^2-32 x^3\right )+e^{-x^2+x^3} \left (-136 x^2+136 x^3-34 x^4+e^{-\frac {x}{-2+x}} \left (-32-128 x+320 x^2-224 x^3+48 x^4\right )\right )}{64 x^4-64 x^5+16 x^6+e^{-2 x^2+2 x^3} \left (64-64 x+16 x^2\right )+e^{-x^2+x^3} \left (-128 x^2+128 x^3-32 x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 x^2} \left (68 x^4-68 x^5+17 x^6+e^{-2 x^2+2 x^3} \left (68-68 x+17 x^2\right )+e^{-\frac {x}{-2+x}} \left (-128 x+160 x^2-32 x^3\right )+e^{-x^2+x^3} \left (-136 x^2+136 x^3-34 x^4+e^{-\frac {x}{-2+x}} \left (-32-128 x+320 x^2-224 x^3+48 x^4\right )\right )\right )}{16 (2-x)^2 \left (e^{x^3}-e^{x^2} x^2\right )^2} \, dx\\ &=\frac {1}{16} \int \frac {e^{2 x^2} \left (68 x^4-68 x^5+17 x^6+e^{-2 x^2+2 x^3} \left (68-68 x+17 x^2\right )+e^{-\frac {x}{-2+x}} \left (-128 x+160 x^2-32 x^3\right )+e^{-x^2+x^3} \left (-136 x^2+136 x^3-34 x^4+e^{-\frac {x}{-2+x}} \left (-32-128 x+320 x^2-224 x^3+48 x^4\right )\right )\right )}{(2-x)^2 \left (e^{x^3}-e^{x^2} x^2\right )^2} \, dx\\ &=\frac {1}{16} \int \left (17+\frac {16 e^{-\frac {x}{-2+x}+2 x^2} x \left (-2-2 x^2+3 x^3\right )}{\left (-e^{x^3}+e^{x^2} x^2\right )^2}+\frac {16 e^{-\frac {(-1+x)^2 x}{-2+x}+2 x^2} \left (-2-8 x+20 x^2-14 x^3+3 x^4\right )}{(2-x)^2 \left (e^{x^3}-e^{x^2} x^2\right )}\right ) \, dx\\ &=\frac {17 x}{16}+\int \frac {e^{-\frac {x}{-2+x}+2 x^2} x \left (-2-2 x^2+3 x^3\right )}{\left (-e^{x^3}+e^{x^2} x^2\right )^2} \, dx+\int \frac {e^{-\frac {(-1+x)^2 x}{-2+x}+2 x^2} \left (-2-8 x+20 x^2-14 x^3+3 x^4\right )}{(2-x)^2 \left (e^{x^3}-e^{x^2} x^2\right )} \, dx\\ &=\frac {17 x}{16}+\int \frac {e^{\frac {x \left (-1-2 x+x^2\right )}{-2+x}} \left (-2-8 x+20 x^2-14 x^3+3 x^4\right )}{(2-x)^2 \left (e^{x^3}-e^{x^2} x^2\right )} \, dx+\int \left (-\frac {2 e^{-\frac {x}{-2+x}+2 x^2} x}{\left (-e^{x^3}+e^{x^2} x^2\right )^2}-\frac {2 e^{-\frac {x}{-2+x}+2 x^2} x^3}{\left (-e^{x^3}+e^{x^2} x^2\right )^2}+\frac {3 e^{-\frac {x}{-2+x}+2 x^2} x^4}{\left (-e^{x^3}+e^{x^2} x^2\right )^2}\right ) \, dx\\ &=\frac {17 x}{16}-2 \int \frac {e^{-\frac {x}{-2+x}+2 x^2} x}{\left (-e^{x^3}+e^{x^2} x^2\right )^2} \, dx-2 \int \frac {e^{-\frac {x}{-2+x}+2 x^2} x^3}{\left (-e^{x^3}+e^{x^2} x^2\right )^2} \, dx+3 \int \frac {e^{-\frac {x}{-2+x}+2 x^2} x^4}{\left (-e^{x^3}+e^{x^2} x^2\right )^2} \, dx+\int \left (\frac {2 e^{\frac {x \left (-1-2 x+x^2\right )}{-2+x}}}{(-2+x)^2 \left (-e^{x^3}+e^{x^2} x^2\right )}+\frac {2 e^{\frac {x \left (-1-2 x+x^2\right )}{-2+x}} x}{-e^{x^3}+e^{x^2} x^2}-\frac {3 e^{\frac {x \left (-1-2 x+x^2\right )}{-2+x}} x^2}{-e^{x^3}+e^{x^2} x^2}\right ) \, dx\\ &=\frac {17 x}{16}-2 \int \frac {e^{-\frac {x}{-2+x}+2 x^2} x}{\left (-e^{x^3}+e^{x^2} x^2\right )^2} \, dx-2 \int \frac {e^{-\frac {x}{-2+x}+2 x^2} x^3}{\left (-e^{x^3}+e^{x^2} x^2\right )^2} \, dx+2 \int \frac {e^{\frac {x \left (-1-2 x+x^2\right )}{-2+x}}}{(-2+x)^2 \left (-e^{x^3}+e^{x^2} x^2\right )} \, dx+2 \int \frac {e^{\frac {x \left (-1-2 x+x^2\right )}{-2+x}} x}{-e^{x^3}+e^{x^2} x^2} \, dx+3 \int \frac {e^{-\frac {x}{-2+x}+2 x^2} x^4}{\left (-e^{x^3}+e^{x^2} x^2\right )^2} \, dx-3 \int \frac {e^{\frac {x \left (-1-2 x+x^2\right )}{-2+x}} x^2}{-e^{x^3}+e^{x^2} x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.21, size = 42, normalized size = 1.17 \begin {gather*} \frac {1}{16} \left (17 x-\frac {16 e^{-1-\frac {2}{-2+x}+x^2}}{e^{x^3}-e^{x^2} x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {\left (17 x^{2}-68 x +68\right ) {\mathrm e}^{2 x^{3}-2 x^{2}}+\left (\left (48 x^{4}-224 x^{3}+320 x^{2}-128 x -32\right ) {\mathrm e}^{-\frac {x}{x -2}}-34 x^{4}+136 x^{3}-136 x^{2}\right ) {\mathrm e}^{x^{3}-x^{2}}+\left (-32 x^{3}+160 x^{2}-128 x \right ) {\mathrm e}^{-\frac {x}{x -2}}+17 x^{6}-68 x^{5}+68 x^{4}}{\left (16 x^{2}-64 x +64\right ) {\mathrm e}^{2 x^{3}-2 x^{2}}+\left (-32 x^{4}+128 x^{3}-128 x^{2}\right ) {\mathrm e}^{x^{3}-x^{2}}+16 x^{6}-64 x^{5}+64 x^{4}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 58, normalized size = 1.61 \begin {gather*} \frac {17 \, x^{3} e^{\left (x^{2} + 1\right )} - 17 \, x e^{\left (x^{3} + 1\right )} + 16 \, e^{\left (x^{2} - \frac {2}{x - 2}\right )}}{16 \, {\left (x^{2} e^{\left (x^{2} + 1\right )} - e^{\left (x^{3} + 1\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 50, normalized size = 1.39 \begin {gather*} \frac {17 \, x^{3} - 17 \, x e^{\left (x^{3} - x^{2}\right )} + 16 \, e^{\left (-\frac {x}{x - 2}\right )}}{16 \, {\left (x^{2} - e^{\left (x^{3} - x^{2}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 24, normalized size = 0.67 \begin {gather*} \frac {17 x}{16} - \frac {e^{- \frac {x}{x - 2}}}{- x^{2} + e^{x^{3} - x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.24, size = 33, normalized size = 0.92 \begin {gather*} \frac {17\,x}{16}-\frac {{\mathrm {e}}^{-\frac {x}{x-2}}}{{\mathrm {e}}^{x^3-x^2}-x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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