Optimal. Leaf size=24 \[ e^{x-\left (-\frac {10+e^{225 x/16}}{x}+x\right )^2} \]
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Rubi [F] time = 11.57, 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 {-100-e^{225 x/8}+20 x^2+x^3-x^4+e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \left (1600+e^{225 x/8} (16-225 x)+8 x^3-16 x^4+e^{225 x/16} \left (320-2250 x+225 x^3\right )\right )}{8 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \frac {\exp \left (\frac {-100-e^{225 x/8}+20 x^2+x^3-x^4+e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \left (1600+e^{225 x/8} (16-225 x)+8 x^3-16 x^4+e^{225 x/16} \left (320-2250 x+225 x^3\right )\right )}{x^3} \, dx\\ &=\frac {1}{8} \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \left (1600+e^{225 x/8} (16-225 x)+8 x^3-16 x^4+e^{225 x/16} \left (320-2250 x+225 x^3\right )\right )}{x^3} \, dx\\ &=\frac {1}{8} \int \left (-\frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {233 x}{8}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) (-16+225 x)}{x^3}+\frac {5 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \left (64-450 x+45 x^3\right )}{x^3}-\frac {8 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \left (-200-x^3+2 x^4\right )}{x^3}\right ) \, dx\\ &=-\left (\frac {1}{8} \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {233 x}{8}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) (-16+225 x)}{x^3} \, dx\right )+\frac {5}{8} \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \left (64-450 x+45 x^3\right )}{x^3} \, dx-\int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \left (-200-x^3+2 x^4\right )}{x^3} \, dx\\ &=-\left (\frac {1}{8} \int \left (-\frac {16 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {233 x}{8}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^3}+\frac {225 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {233 x}{8}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^2}\right ) \, dx\right )+\frac {5}{8} \int \left (45 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )+\frac {64 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^3}-\frac {450 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^2}\right ) \, dx-\int \left (-\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )-\frac {200 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^3}+2 \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) x\right ) \, dx\\ &=2 \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {233 x}{8}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^3} \, dx-2 \int \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) x \, dx+\frac {225}{8} \int \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \, dx-\frac {225}{8} \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {233 x}{8}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^2} \, dx+40 \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^3} \, dx+200 \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^3} \, dx-\frac {1125}{4} \int \frac {\exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+\frac {241 x}{16}-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right )}{x^2} \, dx+\int \exp \left (20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {e^{225 x/16} \left (-20+2 x^2\right )}{x^2}\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 44, normalized size = 1.83 \begin {gather*} e^{20-\frac {100}{x^2}-\frac {e^{225 x/8}}{x^2}+x-x^2+\frac {2 e^{225 x/16} \left (-10+x^2\right )}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 36, normalized size = 1.50 \begin {gather*} e^{\left (-\frac {x^{4} - x^{3} - 20 \, x^{2} - 2 \, {\left (x^{2} - 10\right )} e^{\left (\frac {225}{16} \, x\right )} + e^{\left (\frac {225}{8} \, x\right )} + 100}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 38, normalized size = 1.58 \begin {gather*} e^{\left (-x^{2} + x - \frac {e^{\left (\frac {225}{8} \, x\right )}}{x^{2}} - \frac {20 \, e^{\left (\frac {225}{16} \, x\right )}}{x^{2}} - \frac {100}{x^{2}} + 2 \, e^{\left (\frac {225}{16} \, x\right )} + 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 41, normalized size = 1.71
method | result | size |
norman | \({\mathrm e}^{\frac {-{\mathrm e}^{\frac {225 x}{8}}+\left (2 x^{2}-20\right ) {\mathrm e}^{\frac {225 x}{16}}-x^{4}+x^{3}+20 x^{2}-100}{x^{2}}}\) | \(41\) |
risch | \({\mathrm e}^{-\frac {x^{4}-2 \,{\mathrm e}^{\frac {225 x}{16}} x^{2}-x^{3}-20 x^{2}+20 \,{\mathrm e}^{\frac {225 x}{16}}+{\mathrm e}^{\frac {225 x}{8}}+100}{x^{2}}}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {1}{8} \, \int \frac {{\left (16 \, x^{4} - 8 \, x^{3} + {\left (225 \, x - 16\right )} e^{\left (\frac {225}{8} \, x\right )} - 5 \, {\left (45 \, x^{3} - 450 \, x + 64\right )} e^{\left (\frac {225}{16} \, x\right )} - 1600\right )} e^{\left (-\frac {x^{4} - x^{3} - 20 \, x^{2} - 2 \, {\left (x^{2} - 10\right )} e^{\left (\frac {225}{16} \, x\right )} + e^{\left (\frac {225}{8} \, x\right )} + 100}{x^{2}}\right )}}{x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.56, size = 44, normalized size = 1.83 \begin {gather*} {\mathrm {e}}^{2\,{\mathrm {e}}^{\frac {225\,x}{16}}}\,{\mathrm {e}}^{20}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{-\frac {100}{x^2}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{\frac {225\,x}{8}}}{x^2}}\,{\mathrm {e}}^{-\frac {20\,{\mathrm {e}}^{\frac {225\,x}{16}}}{x^2}}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.37, size = 37, normalized size = 1.54 \begin {gather*} e^{\frac {- x^{4} + x^{3} + 20 x^{2} + \left (2 x^{2} - 20\right ) e^{\frac {225 x}{16}} - e^{\frac {225 x}{8}} - 100}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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