Optimal. Leaf size=35 \[ x-\frac {\left (-3+\frac {9}{4 x^2}-x-x \left (1-x-e^6 x\right )\right )^2}{x} \]
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Rubi [A] time = 0.05, antiderivative size = 64, normalized size of antiderivative = 1.83, number of steps used = 4, number of rules used = 3, integrand size = 72, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {6, 12, 14} \begin {gather*} -\frac {81}{16 x^5}-\left (1+e^6\right )^2 x^3+\frac {27}{2 x^3}+4 \left (1+e^6\right ) x^2+\frac {9}{x^2}+3 \left (1+2 e^6\right ) x-\frac {9 \left (3+e^6\right )}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {405-648 x^2-288 x^3+216 x^4+48 x^6+128 x^7+\left (-48-48 e^{12}\right ) x^8+e^6 \left (72 x^4+96 x^6+128 x^7-96 x^8\right )}{16 x^6} \, dx\\ &=\frac {1}{16} \int \frac {405-648 x^2-288 x^3+216 x^4+48 x^6+128 x^7+\left (-48-48 e^{12}\right ) x^8+e^6 \left (72 x^4+96 x^6+128 x^7-96 x^8\right )}{x^6} \, dx\\ &=\frac {1}{16} \int \left (48 \left (1+2 e^6\right )+\frac {405}{x^6}-\frac {648}{x^4}-\frac {288}{x^3}+\frac {72 \left (3+e^6\right )}{x^2}+128 \left (1+e^6\right ) x-48 \left (1+e^6\right )^2 x^2\right ) \, dx\\ &=-\frac {81}{16 x^5}+\frac {27}{2 x^3}+\frac {9}{x^2}-\frac {9 \left (3+e^6\right )}{2 x}+3 \left (1+2 e^6\right ) x+4 \left (1+e^6\right ) x^2-\left (1+e^6\right )^2 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 63, normalized size = 1.80 \begin {gather*} -\frac {81}{16 x^5}+\frac {27}{2 x^3}+\frac {9}{x^2}-\frac {9 \left (3+e^6\right )}{2 x}+3 x+6 e^6 x+4 \left (1+e^6\right ) x^2-\left (1+e^6\right )^2 x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.10, size = 69, normalized size = 1.97 \begin {gather*} -\frac {16 \, x^{8} e^{12} + 16 \, x^{8} - 64 \, x^{7} - 48 \, x^{6} + 216 \, x^{4} - 144 \, x^{3} - 216 \, x^{2} + 8 \, {\left (4 \, x^{8} - 8 \, x^{7} - 12 \, x^{6} + 9 \, x^{4}\right )} e^{6} + 81}{16 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 69, normalized size = 1.97 \begin {gather*} -x^{3} e^{12} - 2 \, x^{3} e^{6} - x^{3} + 4 \, x^{2} e^{6} + 4 \, x^{2} + 6 \, x e^{6} + 3 \, x - \frac {9 \, {\left (8 \, x^{4} e^{6} + 24 \, x^{4} - 16 \, x^{3} - 24 \, x^{2} + 9\right )}}{16 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 67, normalized size = 1.91
method | result | size |
default | \(-x^{3} {\mathrm e}^{12}-2 x^{3} {\mathrm e}^{6}+4 x^{2} {\mathrm e}^{6}-x^{3}+6 x \,{\mathrm e}^{6}+4 x^{2}+3 x -\frac {81}{16 x^{5}}-\frac {72 \,{\mathrm e}^{6}+216}{16 x}+\frac {9}{x^{2}}+\frac {27}{2 x^{3}}\) | \(67\) |
risch | \(-x^{3} {\mathrm e}^{12}-2 x^{3} {\mathrm e}^{6}+4 x^{2} {\mathrm e}^{6}+6 x \,{\mathrm e}^{6}-x^{3}+4 x^{2}+3 x +\frac {\left (-72 \,{\mathrm e}^{6}-216\right ) x^{4}+144 x^{3}+216 x^{2}-81}{16 x^{5}}\) | \(68\) |
norman | \(\frac {-\frac {81}{16}+\left (4 \,{\mathrm e}^{6}+4\right ) x^{7}+\left (6 \,{\mathrm e}^{6}+3\right ) x^{6}+\left (-\frac {9 \,{\mathrm e}^{6}}{2}-\frac {27}{2}\right ) x^{4}+\left (-{\mathrm e}^{12}-2 \,{\mathrm e}^{6}-1\right ) x^{8}+\frac {27 x^{2}}{2}+9 x^{3}}{x^{5}}\) | \(71\) |
gosper | \(-\frac {16 x^{8} {\mathrm e}^{12}+32 \,{\mathrm e}^{6} x^{8}-64 x^{7} {\mathrm e}^{6}-96 x^{6} {\mathrm e}^{6}+16 x^{8}-64 x^{7}+72 x^{4} {\mathrm e}^{6}-48 x^{6}+216 x^{4}-144 x^{3}-216 x^{2}+81}{16 x^{5}}\) | \(83\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 58, normalized size = 1.66 \begin {gather*} -x^{3} {\left (e^{12} + 2 \, e^{6} + 1\right )} + 4 \, x^{2} {\left (e^{6} + 1\right )} + 3 \, x {\left (2 \, e^{6} + 1\right )} - \frac {9 \, {\left (8 \, x^{4} {\left (e^{6} + 3\right )} - 16 \, x^{3} - 24 \, x^{2} + 9\right )}}{16 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.51, size = 57, normalized size = 1.63 \begin {gather*} x^2\,\left (4\,{\mathrm {e}}^6+4\right )-x^3\,{\left ({\mathrm {e}}^6+1\right )}^2-\frac {\left (72\,{\mathrm {e}}^6+216\right )\,x^4-144\,x^3-216\,x^2+81}{16\,x^5}+x\,\left (6\,{\mathrm {e}}^6+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.45, size = 70, normalized size = 2.00 \begin {gather*} - \frac {x^{3} \left (16 + 32 e^{6} + 16 e^{12}\right )}{16} - \frac {x^{2} \left (- 64 e^{6} - 64\right )}{16} - \frac {x \left (- 96 e^{6} - 48\right )}{16} - \frac {x^{4} \left (216 + 72 e^{6}\right ) - 144 x^{3} - 216 x^{2} + 81}{16 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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