Optimal. Leaf size=31 \[ 7+e^3+e^{-\frac {e^x}{5-e^{-3+x}}+\frac {3+x}{x}} \]
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Rubi [F] time = 11.08, 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 {\exp \left (\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right ) \left (-75+30 e^{-3+x}-3 e^{-6+2 x}-5 e^x x^2\right )}{25 x^2-10 e^{-3+x} x^2+e^{-6+2 x} 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 \frac {\exp \left (6+\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right ) \left (-75+30 e^{-3+x}-3 e^{-6+2 x}-5 e^x x^2\right )}{\left (5 e^3-e^x\right )^2 x^2} \, dx\\ &=\int \left (-\frac {25 \exp \left (9+\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right )}{\left (5 e^3-e^x\right )^2}-\frac {5 \exp \left (6+\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right )}{-5 e^3+e^x}-\frac {3 \exp \left (\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right )}{x^2}\right ) \, dx\\ &=-\left (3 \int \frac {\exp \left (\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right )}{x^2} \, dx\right )-5 \int \frac {\exp \left (6+\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right )}{-5 e^3+e^x} \, dx-25 \int \frac {\exp \left (9+\frac {-15-5 x+e^x x+e^{-3+x} (3+x)}{-5 x+e^{-3+x} x}\right )}{\left (5 e^3-e^x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 28, normalized size = 0.90 \begin {gather*} e^{1+e^3+\frac {5 e^6}{-5 e^3+e^x}+\frac {3}{x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 34, normalized size = 1.10 \begin {gather*} e^{\left (\frac {5 \, {\left (x + 3\right )} e^{3} - {\left (x e^{3} + x + 3\right )} e^{x}}{5 \, x e^{3} - x e^{x}}\right )} \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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maple [A] time = 0.38, size = 35, normalized size = 1.13
method | result | size |
risch | \({\mathrm e}^{\frac {{\mathrm e}^{x} x +x \,{\mathrm e}^{x -3}+3 \,{\mathrm e}^{x -3}-5 x -15}{x \left ({\mathrm e}^{x -3}-5\right )}}\) | \(35\) |
norman | \(\frac {\left (5 x \,{\mathrm e}^{6} {\mathrm e}^{\frac {{\mathrm e}^{x} x +\left (3+x \right ) {\mathrm e}^{-3} {\mathrm e}^{x}-5 x -15}{{\mathrm e}^{-3} {\mathrm e}^{x} x -5 x}}-x \,{\mathrm e}^{3} {\mathrm e}^{x} {\mathrm e}^{\frac {{\mathrm e}^{x} x +\left (3+x \right ) {\mathrm e}^{-3} {\mathrm e}^{x}-5 x -15}{{\mathrm e}^{-3} {\mathrm e}^{x} x -5 x}}\right ) {\mathrm e}^{-3}}{x \left (5 \,{\mathrm e}^{3}-{\mathrm e}^{x}\right )}\) | \(97\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.53, size = 83, normalized size = 2.68 \begin {gather*} e^{\left (\frac {15 \, e^{3}}{5 \, x e^{3} - x e^{x}} + \frac {5 \, e^{3}}{5 \, e^{3} - e^{x}} - \frac {e^{\left (x + 3\right )}}{5 \, e^{3} - e^{x}} - \frac {3 \, e^{x}}{5 \, x e^{3} - x e^{x}} - \frac {e^{x}}{5 \, e^{3} - e^{x}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.43, size = 87, normalized size = 2.81 \begin {gather*} {\mathrm {e}}^{-\frac {3\,{\mathrm {e}}^x}{5\,x\,{\mathrm {e}}^3-x\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^x}{5\,{\mathrm {e}}^3-{\mathrm {e}}^x}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^3\,{\mathrm {e}}^x}{5\,{\mathrm {e}}^3-{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {15\,{\mathrm {e}}^3}{5\,x\,{\mathrm {e}}^3-x\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{\frac {5\,{\mathrm {e}}^3}{5\,{\mathrm {e}}^3-{\mathrm {e}}^x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.53, size = 32, normalized size = 1.03 \begin {gather*} e^{\frac {x e^{x} - 5 x + \frac {\left (x + 3\right ) e^{x}}{e^{3}} - 15}{\frac {x e^{x}}{e^{3}} - 5 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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