Optimal. Leaf size=30 \[ x^2 \left (10+\frac {2}{x}-\frac {x}{25}+\frac {1}{3} \left (-1-e^8+x\right )\right )^2 \]
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Rubi [B] time = 0.02, antiderivative size = 62, normalized size of antiderivative = 2.07, number of steps used = 4, number of rules used = 2, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {6, 12} \begin {gather*} \frac {484 x^4}{5625}-\frac {44 e^8 x^3}{225}+\frac {1276 x^3}{225}+\frac {1}{225} \left (21289+25 e^{16}\right ) x^2-\frac {58 e^8 x^2}{9}-\frac {4 e^8 x}{3}+\frac {116 x}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {217500+\left (1064450+1250 e^{16}\right ) x+95700 x^2+1936 x^3+e^8 \left (-7500-72500 x-3300 x^2\right )}{5625} \, dx\\ &=\frac {\int \left (217500+\left (1064450+1250 e^{16}\right ) x+95700 x^2+1936 x^3+e^8 \left (-7500-72500 x-3300 x^2\right )\right ) \, dx}{5625}\\ &=\frac {116 x}{3}+\frac {1}{225} \left (21289+25 e^{16}\right ) x^2+\frac {1276 x^3}{225}+\frac {484 x^4}{5625}+\frac {e^8 \int \left (-7500-72500 x-3300 x^2\right ) \, dx}{5625}\\ &=\frac {116 x}{3}-\frac {4 e^8 x}{3}-\frac {58 e^8 x^2}{9}+\frac {1}{225} \left (21289+25 e^{16}\right ) x^2+\frac {1276 x^3}{225}-\frac {44 e^8 x^3}{225}+\frac {484 x^4}{5625}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 57, normalized size = 1.90 \begin {gather*} \frac {2 \left (108750 x-3750 e^8 x+\frac {532225 x^2}{2}-18125 e^8 x^2+\frac {625 e^{16} x^2}{2}+15950 x^3-550 e^8 x^3+242 x^4\right )}{5625} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 44, normalized size = 1.47 \begin {gather*} \frac {484}{5625} \, x^{4} + \frac {1276}{225} \, x^{3} + \frac {1}{9} \, x^{2} e^{16} + \frac {21289}{225} \, x^{2} - \frac {2}{225} \, {\left (22 \, x^{3} + 725 \, x^{2} + 150 \, x\right )} e^{8} + \frac {116}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.14, size = 44, normalized size = 1.47 \begin {gather*} \frac {484}{5625} \, x^{4} + \frac {1276}{225} \, x^{3} + \frac {1}{9} \, x^{2} e^{16} + \frac {21289}{225} \, x^{2} - \frac {2}{225} \, {\left (22 \, x^{3} + 725 \, x^{2} + 150 \, x\right )} e^{8} + \frac {116}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 41, normalized size = 1.37
method | result | size |
norman | \(\left (-\frac {44 \,{\mathrm e}^{8}}{225}+\frac {1276}{225}\right ) x^{3}+\left (-\frac {4 \,{\mathrm e}^{8}}{3}+\frac {116}{3}\right ) x +\left (\frac {{\mathrm e}^{16}}{9}-\frac {58 \,{\mathrm e}^{8}}{9}+\frac {21289}{225}\right ) x^{2}+\frac {484 x^{4}}{5625}\) | \(41\) |
gosper | \(\frac {x \left (625 x \,{\mathrm e}^{16}-1100 x^{2} {\mathrm e}^{8}+484 x^{3}-36250 x \,{\mathrm e}^{8}+31900 x^{2}-7500 \,{\mathrm e}^{8}+532225 x +217500\right )}{5625}\) | \(42\) |
risch | \(\frac {x^{2} {\mathrm e}^{16}}{9}-\frac {44 x^{3} {\mathrm e}^{8}}{225}-\frac {58 x^{2} {\mathrm e}^{8}}{9}-\frac {4 x \,{\mathrm e}^{8}}{3}+\frac {484 x^{4}}{5625}+\frac {1276 x^{3}}{225}+\frac {21289 x^{2}}{225}+\frac {116 x}{3}\) | \(46\) |
default | \(\frac {x^{2} {\mathrm e}^{16}}{9}+\frac {{\mathrm e}^{8} \left (-1100 x^{3}-36250 x^{2}-7500 x \right )}{5625}+\frac {484 x^{4}}{5625}+\frac {1276 x^{3}}{225}+\frac {21289 x^{2}}{225}+\frac {116 x}{3}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 44, normalized size = 1.47 \begin {gather*} \frac {484}{5625} \, x^{4} + \frac {1276}{225} \, x^{3} + \frac {1}{9} \, x^{2} e^{16} + \frac {21289}{225} \, x^{2} - \frac {2}{225} \, {\left (22 \, x^{3} + 725 \, x^{2} + 150 \, x\right )} e^{8} + \frac {116}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.09, size = 40, normalized size = 1.33 \begin {gather*} \frac {484\,x^4}{5625}+\left (\frac {1276}{225}-\frac {44\,{\mathrm {e}}^8}{225}\right )\,x^3+\left (\frac {{\mathrm {e}}^{16}}{9}-\frac {58\,{\mathrm {e}}^8}{9}+\frac {21289}{225}\right )\,x^2+\left (\frac {116}{3}-\frac {4\,{\mathrm {e}}^8}{3}\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 49, normalized size = 1.63 \begin {gather*} \frac {484 x^{4}}{5625} + x^{3} \left (\frac {1276}{225} - \frac {44 e^{8}}{225}\right ) + x^{2} \left (- \frac {58 e^{8}}{9} + \frac {21289}{225} + \frac {e^{16}}{9}\right ) + x \left (\frac {116}{3} - \frac {4 e^{8}}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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