Optimal. Leaf size=31 \[ \frac {2}{5-\left (-3+\frac {5-e^{6 x^4} (-5+x)+x}{x}\right )^2} \]
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Rubi [F] time = 66.12, 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 {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 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 {4 x \left (5 (-5+2 x)+e^{12 x^4} \left (-25+5 x+600 x^4-240 x^5+24 x^6\right )+e^{6 x^4} \left (-50+15 x+600 x^4-360 x^5+48 x^6\right )\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=4 \int \frac {x \left (5 (-5+2 x)+e^{12 x^4} \left (-25+5 x+600 x^4-240 x^5+24 x^6\right )+e^{6 x^4} \left (-50+15 x+600 x^4-360 x^5+48 x^6\right )\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=4 \int \left (\frac {x \left (5-120 x^4+24 x^5\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )}-\frac {x^2 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}\right ) \, dx\\ &=4 \int \frac {x \left (5-120 x^4+24 x^5\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )} \, dx-4 \int \frac {x^2 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx\\ &=4 \int \frac {x \left (-5+120 x^4-24 x^5\right )}{(5-x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )} \, dx-4 \int \frac {x^2 \left (25+15 x+3000 x^3-3000 x^4+360 x^5+24 x^6-e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )\right )}{(5-x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=4 \int \left (\frac {5}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2}+\frac {25}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )}+\frac {24 x^5}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2}\right ) \, dx-4 \int \left (\frac {5 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}+\frac {25 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}+\frac {x \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}\right ) \, dx\\ &=-\left (4 \int \frac {x \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx\right )+20 \int \frac {1}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2} \, dx-20 \int \frac {-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx+96 \int \frac {x^5}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2} \, dx+100 \int \frac {1}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )} \, dx-100 \int \frac {-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx\\ &=-\left (4 \int \frac {x \left (-25-15 x-3000 x^3+3000 x^4-360 x^5-24 x^6+e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\right )+20 \int \frac {1}{25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )} \, dx-20 \int \frac {-25-15 x-3000 x^3+3000 x^4-360 x^5-24 x^6+e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx+96 \int \frac {x^5}{25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )} \, dx+100 \int \frac {1}{(-5+x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )} \, dx-100 \int \frac {25+15 x+3000 x^3-3000 x^4+360 x^5+24 x^6-e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )}{(5-x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 48, normalized size = 1.55 \begin {gather*} -\frac {2 x^2}{25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 49, normalized size = 1.58 \begin {gather*} \frac {2 \, x^{2}}{x^{2} - {\left (x^{2} - 10 \, x + 25\right )} e^{\left (12 \, x^{4}\right )} - 2 \, {\left (2 \, x^{2} - 15 \, x + 25\right )} e^{\left (6 \, x^{4}\right )} + 20 \, x - 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 73, normalized size = 2.35
method | result | size |
risch | \(-\frac {2 x^{2}}{{\mathrm e}^{12 x^{4}} x^{2}-10 \,{\mathrm e}^{12 x^{4}} x +4 \,{\mathrm e}^{6 x^{4}} x^{2}+25 \,{\mathrm e}^{12 x^{4}}-30 \,{\mathrm e}^{6 x^{4}} x -x^{2}+50 \,{\mathrm e}^{6 x^{4}}-20 x +25}\) | \(73\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 49, normalized size = 1.58 \begin {gather*} \frac {2 \, x^{2}}{x^{2} - {\left (x^{2} - 10 \, x + 25\right )} e^{\left (12 \, x^{4}\right )} - 2 \, {\left (2 \, x^{2} - 15 \, x + 25\right )} e^{\left (6 \, x^{4}\right )} + 20 \, x - 25} \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}}^{12\,x^4}\,\left (96\,x^7-960\,x^6+2400\,x^5+20\,x^2-100\,x\right )-100\,x+{\mathrm {e}}^{6\,x^4}\,\left (192\,x^7-1440\,x^6+2400\,x^5+60\,x^2-200\,x\right )+40\,x^2}{{\mathrm {e}}^{24\,x^4}\,\left (x^4-20\,x^3+150\,x^2-500\,x+625\right )-1000\,x+{\mathrm {e}}^{18\,x^4}\,\left (8\,x^4-140\,x^3+900\,x^2-2500\,x+2500\right )-{\mathrm {e}}^{6\,x^4}\,\left (8\,x^4+100\,x^3-1300\,x^2+3500\,x-2500\right )+{\mathrm {e}}^{12\,x^4}\,\left (14\,x^4-260\,x^3+1700\,x^2-4500\,x+3750\right )+350\,x^2+40\,x^3+x^4+625} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.54, size = 46, normalized size = 1.48 \begin {gather*} - \frac {2 x^{2}}{- x^{2} - 20 x + \left (x^{2} - 10 x + 25\right ) e^{12 x^{4}} + \left (4 x^{2} - 30 x + 50\right ) e^{6 x^{4}} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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