Optimal. Leaf size=28 \[ \frac {e^{-5+\frac {2}{x^2}+\frac {4}{x (3+x)}}}{35 (5+x)} \]
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Rubi [F] time = 2.03, 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 {e^{\frac {6+6 x-15 x^2-5 x^3}{3 x^2+x^3}} \left (-180-216 x-96 x^2-21 x^3-6 x^4-x^5\right )}{7875 x^3+8400 x^4+3290 x^5+560 x^6+35 x^7} \, 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^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}} \left (-180-216 x-96 x^2-21 x^3-6 x^4-x^5\right )}{35 x^3 \left (15+8 x+x^2\right )^2} \, dx\\ &=\frac {1}{35} \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}} \left (-180-216 x-96 x^2-21 x^3-6 x^4-x^5\right )}{x^3 \left (15+8 x+x^2\right )^2} \, dx\\ &=\frac {1}{35} \int \left (-\frac {4 e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{5 x^3}-\frac {8 e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{75 x^2}+\frac {8 e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{375 x}+\frac {2 e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{3 (3+x)^2}-\frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{3 (3+x)}-\frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{(5+x)^2}+\frac {39 e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{125 (5+x)}\right ) \, dx\\ &=\frac {8 \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{x} \, dx}{13125}-\frac {8 \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{x^2} \, dx}{2625}+\frac {39 \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{5+x} \, dx}{4375}-\frac {1}{105} \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{3+x} \, dx+\frac {2}{105} \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{(3+x)^2} \, dx-\frac {4}{175} \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{x^3} \, dx-\frac {1}{35} \int \frac {e^{\frac {6+6 x-15 x^2-5 x^3}{x^2 (3+x)}}}{(5+x)^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.44, size = 34, normalized size = 1.21 \begin {gather*} \frac {e^{-5+\frac {2}{x^2}+\frac {4}{3 x}-\frac {4}{3 (3+x)}}}{35 (5+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.08, size = 36, normalized size = 1.29 \begin {gather*} \frac {e^{\left (-\frac {5 \, x^{3} + 15 \, x^{2} - 6 \, x - 6}{x^{3} + 3 \, x^{2}}\right )}}{35 \, {\left (x + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 36, normalized size = 1.29 \begin {gather*} \frac {e^{\left (-\frac {5 \, x^{3} + 15 \, x^{2} - 6 \, x - 6}{x^{3} + 3 \, x^{2}}\right )}}{35 \, {\left (x + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 34, normalized size = 1.21
method | result | size |
gosper | \(\frac {{\mathrm e}^{-\frac {5 x^{3}+15 x^{2}-6 x -6}{x^{2} \left (3+x \right )}}}{175+35 x}\) | \(34\) |
risch | \(\frac {{\mathrm e}^{-\frac {5 x^{3}+15 x^{2}-6 x -6}{x^{2} \left (3+x \right )}}}{175+35 x}\) | \(34\) |
norman | \(\frac {\frac {3 x^{2} {\mathrm e}^{\frac {-5 x^{3}-15 x^{2}+6 x +6}{x^{3}+3 x^{2}}}}{35}+\frac {x^{3} {\mathrm e}^{\frac {-5 x^{3}-15 x^{2}+6 x +6}{x^{3}+3 x^{2}}}}{35}}{x^{2} \left (x^{2}+8 x +15\right )}\) | \(82\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 32, normalized size = 1.14 \begin {gather*} \frac {e^{\left (-\frac {4}{3 \, {\left (x + 3\right )}} + \frac {4}{3 \, x} + \frac {2}{x^{2}}\right )}}{35 \, {\left (x e^{5} + 5 \, e^{5}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.48, size = 51, normalized size = 1.82 \begin {gather*} \frac {{\mathrm {e}}^{\frac {6}{x^2+3\,x}}\,{\mathrm {e}}^{-\frac {5\,x}{x+3}}\,{\mathrm {e}}^{\frac {6}{x^3+3\,x^2}}\,{\mathrm {e}}^{-\frac {15}{x+3}}}{35\,\left (x+5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 29, normalized size = 1.04 \begin {gather*} \frac {e^{\frac {- 5 x^{3} - 15 x^{2} + 6 x + 6}{x^{3} + 3 x^{2}}}}{35 x + 175} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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