Optimal. Leaf size=33 \[ 4+\frac {x^5}{16 \left (\frac {3 \left (2+\frac {e^{-5+x}}{5}\right )}{5 x}-x\right )^2} \]
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Rubi [F] time = 1.97, 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 {131250 x^6-46875 x^8+e^{-5+x} \left (13125 x^6-3750 x^7\right )}{432000+432 e^{-15+3 x}-1080000 x^2+900000 x^4-250000 x^6+e^{-10+2 x} \left (12960-10800 x^2\right )+e^{-5+x} \left (129600-216000 x^2+90000 x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1875 e^{10} x^6 \left (-e^x (-7+2 x)-5 e^5 \left (-14+5 x^2\right )\right )}{16 \left (3 e^x-5 e^5 \left (-6+5 x^2\right )\right )^3} \, dx\\ &=\frac {1}{16} \left (1875 e^{10}\right ) \int \frac {x^6 \left (-e^x (-7+2 x)-5 e^5 \left (-14+5 x^2\right )\right )}{\left (3 e^x-5 e^5 \left (-6+5 x^2\right )\right )^3} \, dx\\ &=\frac {1}{16} \left (1875 e^{10}\right ) \int \left (\frac {10 e^5 x^7 \left (-6-10 x+5 x^2\right )}{3 \left (-30 e^5-3 e^x+25 e^5 x^2\right )^3}-\frac {x^6 (-7+2 x)}{3 \left (-30 e^5-3 e^x+25 e^5 x^2\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{16} \left (625 e^{10}\right ) \int \frac {x^6 (-7+2 x)}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^2} \, dx\right )+\frac {1}{8} \left (3125 e^{15}\right ) \int \frac {x^7 \left (-6-10 x+5 x^2\right )}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^3} \, dx\\ &=-\left (\frac {1}{16} \left (625 e^{10}\right ) \int \left (-\frac {7 x^6}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^2}+\frac {2 x^7}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^2}\right ) \, dx\right )+\frac {1}{8} \left (3125 e^{15}\right ) \int \left (-\frac {6 x^7}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^3}-\frac {10 x^8}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^3}+\frac {5 x^9}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^3}\right ) \, dx\\ &=-\left (\frac {1}{8} \left (625 e^{10}\right ) \int \frac {x^7}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^2} \, dx\right )+\frac {1}{16} \left (4375 e^{10}\right ) \int \frac {x^6}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^2} \, dx+\frac {1}{8} \left (15625 e^{15}\right ) \int \frac {x^9}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^3} \, dx-\frac {1}{4} \left (9375 e^{15}\right ) \int \frac {x^7}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^3} \, dx-\frac {1}{4} \left (15625 e^{15}\right ) \int \frac {x^8}{\left (-30 e^5-3 e^x+25 e^5 x^2\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.36, size = 31, normalized size = 0.94 \begin {gather*} \frac {625 e^{10} x^7}{16 \left (30 e^5+3 e^x-25 e^5 x^2\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 40, normalized size = 1.21 \begin {gather*} \frac {625 \, x^{7}}{16 \, {\left (625 \, x^{4} - 1500 \, x^{2} - 30 \, {\left (5 \, x^{2} - 6\right )} e^{\left (x - 5\right )} + 9 \, e^{\left (2 \, x - 10\right )} + 900\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 49, normalized size = 1.48 \begin {gather*} \frac {625 \, x^{7} e^{10}}{16 \, {\left (625 \, x^{4} e^{10} - 1500 \, x^{2} e^{10} - 150 \, x^{2} e^{\left (x + 5\right )} + 900 \, e^{10} + 9 \, e^{\left (2 \, x\right )} + 180 \, e^{\left (x + 5\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.53, size = 21, normalized size = 0.64
method | result | size |
risch | \(\frac {625 x^{7}}{16 \left (25 x^{2}-3 \,{\mathrm e}^{x -5}-30\right )^{2}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.42, size = 50, normalized size = 1.52 \begin {gather*} \frac {625 \, x^{7} e^{10}}{16 \, {\left (625 \, x^{4} e^{10} - 1500 \, x^{2} e^{10} - 30 \, {\left (5 \, x^{2} e^{5} - 6 \, e^{5}\right )} e^{x} + 900 \, e^{10} + 9 \, e^{\left (2 \, x\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{x-5}\,\left (13125\,x^6-3750\,x^7\right )+131250\,x^6-46875\,x^8}{432\,{\mathrm {e}}^{3\,x-15}+{\mathrm {e}}^{x-5}\,\left (90000\,x^4-216000\,x^2+129600\right )-{\mathrm {e}}^{2\,x-10}\,\left (10800\,x^2-12960\right )-1080000\,x^2+900000\,x^4-250000\,x^6+432000} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 36, normalized size = 1.09 \begin {gather*} \frac {625 x^{7}}{10000 x^{4} - 24000 x^{2} + \left (2880 - 2400 x^{2}\right ) e^{x - 5} + 144 e^{2 x - 10} + 14400} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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