Optimal. Leaf size=19 \[ 3+e-e^{256+\frac {16}{(-5+x)^4}-x} \]
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Rubi [F] time = 1.36, 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 {160016-128625 x+38900 x^2-5270 x^3+276 x^4-x^5}{625-500 x+150 x^2-20 x^3+x^4}\right ) \left (-3061+3125 x-1250 x^2+250 x^3-25 x^4+x^5\right )}{-3125+3125 x-1250 x^2+250 x^3-25 x^4+x^5} \, 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 (\frac {160016-128625 x+38900 x^2-5270 x^3+276 x^4-x^5}{(-5+x)^4}\right ) \left (3061-3125 x+1250 x^2-250 x^3+25 x^4-x^5\right )}{(5-x)^5} \, dx\\ &=\int \left (\exp \left (\frac {160016-128625 x+38900 x^2-5270 x^3+276 x^4-x^5}{(-5+x)^4}\right )+\frac {64 \exp \left (\frac {160016-128625 x+38900 x^2-5270 x^3+276 x^4-x^5}{(-5+x)^4}\right )}{(-5+x)^5}\right ) \, dx\\ &=64 \int \frac {\exp \left (\frac {160016-128625 x+38900 x^2-5270 x^3+276 x^4-x^5}{(-5+x)^4}\right )}{(-5+x)^5} \, dx+\int \exp \left (\frac {160016-128625 x+38900 x^2-5270 x^3+276 x^4-x^5}{(-5+x)^4}\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.31, size = 16, normalized size = 0.84 \begin {gather*} -e^{256+\frac {16}{(-5+x)^4}-x} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.59, size = 48, normalized size = 2.53 \begin {gather*} -e^{\left (-\frac {x^{5} - 276 \, x^{4} + 5270 \, x^{3} - 38900 \, x^{2} + 128625 \, x - 160016}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 149, normalized size = 7.84 \begin {gather*} -e^{\left (-\frac {x^{5}}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625} + \frac {276 \, x^{4}}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625} - \frac {5270 \, x^{3}}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625} + \frac {38900 \, x^{2}}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625} - \frac {128625 \, x}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625} + \frac {160016}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.53, size = 34, normalized size = 1.79
method | result | size |
risch | \(-{\mathrm e}^{-\frac {x^{5}-276 x^{4}+5270 x^{3}-38900 x^{2}+128625 x -160016}{\left (x -5\right )^{4}}}\) | \(34\) |
gosper | \(-{\mathrm e}^{-\frac {x^{5}-276 x^{4}+5270 x^{3}-38900 x^{2}+128625 x -160016}{x^{4}-20 x^{3}+150 x^{2}-500 x +625}}\) | \(49\) |
norman | \(\frac {500 x \,{\mathrm e}^{\frac {-x^{5}+276 x^{4}-5270 x^{3}+38900 x^{2}-128625 x +160016}{x^{4}-20 x^{3}+150 x^{2}-500 x +625}}-150 x^{2} {\mathrm e}^{\frac {-x^{5}+276 x^{4}-5270 x^{3}+38900 x^{2}-128625 x +160016}{x^{4}-20 x^{3}+150 x^{2}-500 x +625}}+20 x^{3} {\mathrm e}^{\frac {-x^{5}+276 x^{4}-5270 x^{3}+38900 x^{2}-128625 x +160016}{x^{4}-20 x^{3}+150 x^{2}-500 x +625}}-x^{4} {\mathrm e}^{\frac {-x^{5}+276 x^{4}-5270 x^{3}+38900 x^{2}-128625 x +160016}{x^{4}-20 x^{3}+150 x^{2}-500 x +625}}-625 \,{\mathrm e}^{\frac {-x^{5}+276 x^{4}-5270 x^{3}+38900 x^{2}-128625 x +160016}{x^{4}-20 x^{3}+150 x^{2}-500 x +625}}}{\left (x -5\right )^{4}}\) | \(263\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 30, normalized size = 1.58 \begin {gather*} -e^{\left (-x + \frac {16}{x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625} + 256\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.01, size = 153, normalized size = 8.05 \begin {gather*} -{\mathrm {e}}^{-\frac {128625\,x}{x^4-20\,x^3+150\,x^2-500\,x+625}}\,{\mathrm {e}}^{-\frac {x^5}{x^4-20\,x^3+150\,x^2-500\,x+625}}\,{\mathrm {e}}^{\frac {276\,x^4}{x^4-20\,x^3+150\,x^2-500\,x+625}}\,{\mathrm {e}}^{-\frac {5270\,x^3}{x^4-20\,x^3+150\,x^2-500\,x+625}}\,{\mathrm {e}}^{\frac {38900\,x^2}{x^4-20\,x^3+150\,x^2-500\,x+625}}\,{\mathrm {e}}^{\frac {160016}{x^4-20\,x^3+150\,x^2-500\,x+625}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.30, size = 44, normalized size = 2.32 \begin {gather*} - e^{\frac {- x^{5} + 276 x^{4} - 5270 x^{3} + 38900 x^{2} - 128625 x + 160016}{x^{4} - 20 x^{3} + 150 x^{2} - 500 x + 625}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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