Optimal. Leaf size=25 \[ \frac {2}{3 \left (\frac {e^{625 x^6}}{x}-2 x-\log (4)\right )} \]
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Rubi [F] time = 1.47, 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 {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 e^{1250 x^6}+12 x^4+12 x^3 \log (4)+3 x^2 \log ^2(4)+e^{625 x^6} \left (-12 x^2-6 x \log (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^2+e^{625 x^6} \left (2-7500 x^6\right )}{3 \left (e^{625 x^6}-x (2 x+\log (4))\right )^2} \, dx\\ &=\frac {1}{3} \int \frac {4 x^2+e^{625 x^6} \left (2-7500 x^6\right )}{\left (e^{625 x^6}-x (2 x+\log (4))\right )^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {2 \left (-1+3750 x^6\right )}{-e^{625 x^6}+2 x^2+x \log (4)}-\frac {2 x \left (-4 x+7500 x^7-\log (4)+3750 x^6 \log (4)\right )}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}\right ) \, dx\\ &=\frac {2}{3} \int \frac {-1+3750 x^6}{-e^{625 x^6}+2 x^2+x \log (4)} \, dx-\frac {2}{3} \int \frac {x \left (-4 x+7500 x^7-\log (4)+3750 x^6 \log (4)\right )}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx\\ &=-\left (\frac {2}{3} \int \left (-\frac {4 x^2}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}+\frac {7500 x^8}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}-\frac {x \log (4)}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}+\frac {3750 x^7 \log (4)}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2}\right ) \, dx\right )+\frac {2}{3} \int \left (\frac {1}{e^{625 x^6}-2 x^2-x \log (4)}+\frac {3750 x^6}{-e^{625 x^6}+2 x^2+x \log (4)}\right ) \, dx\\ &=\frac {2}{3} \int \frac {1}{e^{625 x^6}-2 x^2-x \log (4)} \, dx+\frac {8}{3} \int \frac {x^2}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx+2500 \int \frac {x^6}{-e^{625 x^6}+2 x^2+x \log (4)} \, dx-5000 \int \frac {x^8}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx+\frac {1}{3} (2 \log (4)) \int \frac {x}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx-(2500 \log (4)) \int \frac {x^7}{\left (-e^{625 x^6}+2 x^2+x \log (4)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.41, size = 25, normalized size = 1.00 \begin {gather*} \frac {2 x}{3 \left (e^{625 x^6}-2 x^2-x \log (4)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 24, normalized size = 0.96 \begin {gather*} -\frac {2 \, x}{3 \, {\left (2 \, x^{2} + 2 \, x \log \relax (2) - e^{\left (625 \, x^{6}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 24, normalized size = 0.96 \begin {gather*} -\frac {2 \, x}{3 \, {\left (2 \, x^{2} + 2 \, x \log \relax (2) - e^{\left (625 \, x^{6}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 25, normalized size = 1.00
method | result | size |
norman | \(-\frac {2 x}{3 \left (2 x \ln \relax (2)+2 x^{2}-{\mathrm e}^{625 x^{6}}\right )}\) | \(25\) |
risch | \(-\frac {2 x}{3 \left (2 x \ln \relax (2)+2 x^{2}-{\mathrm e}^{625 x^{6}}\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 24, normalized size = 0.96 \begin {gather*} -\frac {2 \, x}{3 \, {\left (2 \, x^{2} + 2 \, x \log \relax (2) - e^{\left (625 \, x^{6}\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 = -0.04 \begin {gather*} -\int \frac {{\mathrm {e}}^{625\,x^6}\,\left (7500\,x^6-2\right )-4\,x^2}{3\,{\mathrm {e}}^{1250\,x^6}+12\,x^2\,{\ln \relax (2)}^2+24\,x^3\,\ln \relax (2)-{\mathrm {e}}^{625\,x^6}\,\left (12\,x^2+12\,\ln \relax (2)\,x\right )+12\,x^4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 22, normalized size = 0.88 \begin {gather*} \frac {2 x}{- 6 x^{2} - 6 x \log {\relax (2 )} + 3 e^{625 x^{6}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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