Optimal. Leaf size=22 \[ x^2+\frac {x \left (22+e^{20}+x\right )}{4 (5-x)} \]
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Rubi [A] time = 0.03, antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps used = 4, number of rules used = 3, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {27, 12, 1850} \begin {gather*} x^2-\frac {x}{4}+\frac {5 \left (27+e^{20}\right )}{4 (5-x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {110+5 e^{20}+210 x-81 x^2+8 x^3}{4 (-5+x)^2} \, dx\\ &=\frac {1}{4} \int \frac {110+5 e^{20}+210 x-81 x^2+8 x^3}{(-5+x)^2} \, dx\\ &=\frac {1}{4} \int \left (-1+\frac {5 \left (27+e^{20}\right )}{(-5+x)^2}+8 x\right ) \, dx\\ &=\frac {5 \left (27+e^{20}\right )}{4 (5-x)}-\frac {x}{4}+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.32 \begin {gather*} \frac {1}{4} \left (-\frac {5 \left (27+e^{20}\right )}{-5+x}+39 (-5+x)+4 (-5+x)^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.18, size = 26, normalized size = 1.18 \begin {gather*} \frac {4 \, x^{3} - 21 \, x^{2} + 5 \, x - 5 \, e^{20} - 135}{4 \, {\left (x - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 18, normalized size = 0.82 \begin {gather*} x^{2} - \frac {1}{4} \, x - \frac {5 \, {\left (e^{20} + 27\right )}}{4 \, {\left (x - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.20, size = 21, normalized size = 0.95
method | result | size |
default | \(x^{2}-\frac {x}{4}-\frac {135+5 \,{\mathrm e}^{20}}{4 \left (x -5\right )}\) | \(21\) |
norman | \(\frac {x^{3}-\frac {21 x^{2}}{4}-\frac {55}{2}-\frac {5 \,{\mathrm e}^{20}}{4}}{x -5}\) | \(23\) |
risch | \(x^{2}-\frac {x}{4}-\frac {5 \,{\mathrm e}^{20}}{4 \left (x -5\right )}-\frac {135}{4 \left (x -5\right )}\) | \(24\) |
gosper | \(-\frac {5 \,{\mathrm e}^{20}-4 x^{3}+21 x^{2}+110}{4 \left (x -5\right )}\) | \(26\) |
meijerg | \(\frac {58 x}{5 \left (1-\frac {x}{5}\right )}+\frac {x \,{\mathrm e}^{20}}{-4 x +20}+\frac {5 x \left (-\frac {2}{25} x^{2}-\frac {6}{5} x +12\right )}{2 \left (1-\frac {x}{5}\right )}-\frac {27 x \left (-\frac {3 x}{5}+6\right )}{4 \left (1-\frac {x}{5}\right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 18, normalized size = 0.82 \begin {gather*} x^{2} - \frac {1}{4} \, x - \frac {5 \, {\left (e^{20} + 27\right )}}{4 \, {\left (x - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.51, size = 22, normalized size = 1.00 \begin {gather*} x^2-\frac {5\,{\mathrm {e}}^{20}+135}{4\,x-20}-\frac {x}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 19, normalized size = 0.86 \begin {gather*} x^{2} - \frac {x}{4} + \frac {- 5 e^{20} - 135}{4 x - 20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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