Optimal. Leaf size=24 \[ \frac {160 x^2 \left (\frac {1}{x}-\frac {(4+x)^2}{e^5}\right )}{(-5+x)^2} \]
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Rubi [B] time = 0.07, antiderivative size = 53, normalized size of antiderivative = 2.21, number of steps used = 3, number of rules used = 2, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 2074} \begin {gather*} -\frac {160 x^2}{e^5}-\frac {2880 x}{e^5}+\frac {160 \left (1260-e^5\right )}{e^5 (5-x)}-\frac {800 \left (405-e^5\right )}{e^5 (5-x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^5 (-800-160 x)+25600 x+19200 x^2+1920 x^3-320 x^4}{-125+75 x-15 x^2+x^3} \, dx}{e^5}\\ &=\frac {\int \left (-2880-\frac {1600 \left (-405+e^5\right )}{(-5+x)^3}-\frac {160 \left (-1260+e^5\right )}{(-5+x)^2}-320 x\right ) \, dx}{e^5}\\ &=-\frac {800 \left (405-e^5\right )}{e^5 (5-x)^2}+\frac {160 \left (1260-e^5\right )}{e^5 (5-x)}-\frac {2880 x}{e^5}-\frac {160 x^2}{e^5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 1.38 \begin {gather*} -\frac {160 \left (-7150-\left (-2860+e^5\right ) x-270 x^2+8 x^3+x^4\right )}{e^5 (-5+x)^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 37, normalized size = 1.54 \begin {gather*} -\frac {160 \, {\left (x^{4} + 8 \, x^{3} - 155 \, x^{2} - x e^{5} + 1710 \, x - 4275\right )} e^{\left (-5\right )}}{x^{2} - 10 \, x + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 27, normalized size = 1.12 \begin {gather*} -160 \, {\left (x^{2} + 18 \, x - \frac {x e^{5} - 1260 \, x + 4275}{{\left (x - 5\right )}^{2}}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 36, normalized size = 1.50
method | result | size |
gosper | \(\frac {160 \left (-x^{4}-8 x^{3}+x \,{\mathrm e}^{5}-160 x +400\right ) {\mathrm e}^{-5}}{x^{2}-10 x +25}\) | \(36\) |
risch | \(-160 x^{2} {\mathrm e}^{-5}-2880 x \,{\mathrm e}^{-5}+\frac {{\mathrm e}^{-5} \left (\left (-201600+160 \,{\mathrm e}^{5}\right ) x +684000\right )}{x^{2}-10 x +25}\) | \(37\) |
default | \({\mathrm e}^{-5} \left (-160 x^{2}-2880 x -\frac {160 \left (1260-{\mathrm e}^{5}\right )}{x -5}-\frac {80 \left (-10 \,{\mathrm e}^{5}+4050\right )}{\left (x -5\right )^{2}}\right )\) | \(41\) |
norman | \(\frac {160 \left ({\mathrm e}^{5}-160\right ) {\mathrm e}^{-5} x -1280 \,{\mathrm e}^{-5} x^{3}-160 \,{\mathrm e}^{-5} x^{4}+64000 \,{\mathrm e}^{-5}}{\left (x -5\right )^{2}}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 31, normalized size = 1.29 \begin {gather*} -160 \, {\left (x^{2} + 18 \, x - \frac {x {\left (e^{5} - 1260\right )} + 4275}{x^{2} - 10 \, x + 25}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.32, size = 32, normalized size = 1.33 \begin {gather*} -\frac {160\,{\mathrm {e}}^{-5}\,\left (1710\,x-x\,{\mathrm {e}}^5-155\,x^2+8\,x^3+x^4-4275\right )}{{\left (x-5\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 44, normalized size = 1.83 \begin {gather*} - \frac {160 x^{2}}{e^{5}} - \frac {2880 x}{e^{5}} - \frac {x \left (201600 - 160 e^{5}\right ) - 684000}{x^{2} e^{5} - 10 x e^{5} + 25 e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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