Optimal. Leaf size=22 \[ \frac {3 x^2}{\left (\frac {1}{e^4 \log ^2\left (\frac {5}{3}\right )}-\log (x)\right )^2} \]
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Rubi [C] time = 0.77, antiderivative size = 398, normalized size of antiderivative = 18.09, number of steps used = 12, number of rules used = 7, integrand size = 79, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.089, Rules used = {6688, 12, 2306, 2309, 2178, 2366, 6482} \begin {gather*} 6 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right )+24 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}-4} \left (\frac {1}{\log ^2\left (\frac {5}{3}\right )}-e^4 \log (x)\right ) \text {Ei}\left (2 \log (x)-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}\right )-\frac {6 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}-4} \left (-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)+2-e^4 \log ^2\left (\frac {5}{3}\right )\right ) \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right )}{\log ^2\left (\frac {5}{3}\right )}-\frac {12 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}-4} \left (-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)+1+e^4 \log ^2\left (\frac {5}{3}\right )\right ) \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right )}{\log ^2\left (\frac {5}{3}\right )}+12 x^2-\frac {6 x^2 \left (-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)+1+e^4 \log ^2\left (\frac {5}{3}\right )\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}+\frac {3 e^4 x^2 \log ^2\left (\frac {5}{3}\right ) \left (-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)+1+e^4 \log ^2\left (\frac {5}{3}\right )\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}-\frac {3 x^2 \left (-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)+2-e^4 \log ^2\left (\frac {5}{3}\right )\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2178
Rule 2306
Rule 2309
Rule 2366
Rule 6482
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 e^8 x \log ^4\left (\frac {5}{3}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^3} \, dx\\ &=\left (6 e^8 \log ^4\left (\frac {5}{3}\right )\right ) \int \frac {x \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^3} \, dx\\ &=-\frac {12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}+\frac {3 e^4 x^2 \log ^2\left (\frac {5}{3}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}-\frac {6 x^2 \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}+\left (6 e^{12} \log ^6\left (\frac {5}{3}\right )\right ) \int \left (-\frac {2 e^{-12+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}+2 \log (x)\right )}{x \log ^6\left (\frac {5}{3}\right )}+\frac {x \left (-2 \left (1-\frac {1}{2} e^4 \log ^2\left (\frac {5}{3}\right )\right )+2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{2 e^8 \log ^4\left (\frac {5}{3}\right ) \left (-1+e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}\right ) \, dx\\ &=-\frac {12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}+\frac {3 e^4 x^2 \log ^2\left (\frac {5}{3}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}-\frac {6 x^2 \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\left (12 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}}\right ) \int \frac {\text {Ei}\left (-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}+2 \log (x)\right )}{x} \, dx+\left (3 e^4 \log ^2\left (\frac {5}{3}\right )\right ) \int \frac {x \left (-2 \left (1-\frac {1}{2} e^4 \log ^2\left (\frac {5}{3}\right )\right )+2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (-1+e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2} \, dx\\ &=-\frac {6 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}-\frac {3 x^2 \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\frac {12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}+\frac {3 e^4 x^2 \log ^2\left (\frac {5}{3}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}-\frac {6 x^2 \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\left (12 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}}\right ) \operatorname {Subst}\left (\int \text {Ei}\left (2 x-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \, dx,x,\log (x)\right )-\left (6 e^8 \log ^4\left (\frac {5}{3}\right )\right ) \int \left (\frac {2 e^{-8+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}+2 \log (x)\right )}{x \log ^4\left (\frac {5}{3}\right )}+\frac {x}{e^4 \log ^2\left (\frac {5}{3}\right ) \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}\right ) \, dx\\ &=6 x^2+12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}+2 \log (x)\right ) \left (\frac {1}{\log ^2\left (\frac {5}{3}\right )}-e^4 \log (x)\right )-\frac {6 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}-\frac {3 x^2 \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\frac {12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}+\frac {3 e^4 x^2 \log ^2\left (\frac {5}{3}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}-\frac {6 x^2 \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\left (12 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}}\right ) \int \frac {\text {Ei}\left (-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}+2 \log (x)\right )}{x} \, dx-\left (6 e^4 \log ^2\left (\frac {5}{3}\right )\right ) \int \frac {x}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)} \, dx\\ &=6 x^2+12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}+2 \log (x)\right ) \left (\frac {1}{\log ^2\left (\frac {5}{3}\right )}-e^4 \log (x)\right )-\frac {6 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}-\frac {3 x^2 \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\frac {12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}+\frac {3 e^4 x^2 \log ^2\left (\frac {5}{3}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}-\frac {6 x^2 \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\left (12 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}}\right ) \operatorname {Subst}\left (\int \text {Ei}\left (2 x-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \, dx,x,\log (x)\right )-\left (6 e^4 \log ^2\left (\frac {5}{3}\right )\right ) \operatorname {Subst}\left (\int \frac {e^{2 x}}{1-e^4 x \log ^2\left (\frac {5}{3}\right )} \, dx,x,\log (x)\right )\\ &=12 x^2+6 e^{\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right )+24 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}+2 \log (x)\right ) \left (\frac {1}{\log ^2\left (\frac {5}{3}\right )}-e^4 \log (x)\right )-\frac {6 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}-\frac {3 x^2 \left (2-e^4 \log ^2\left (\frac {5}{3}\right )-2 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}-\frac {12 e^{-4+\frac {2}{e^4 \log ^2\left (\frac {5}{3}\right )}} \text {Ei}\left (-\frac {2 \left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{e^4 \log ^2\left (\frac {5}{3}\right )}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\log ^2\left (\frac {5}{3}\right )}+\frac {3 e^4 x^2 \log ^2\left (\frac {5}{3}\right ) \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}-\frac {6 x^2 \left (1+e^4 \log ^2\left (\frac {5}{3}\right )-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )}{1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 30, normalized size = 1.36 \begin {gather*} \frac {3 e^8 x^2 \log ^4\left (\frac {5}{3}\right )}{\left (-1+e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 36, normalized size = 1.64 \begin {gather*} \frac {3 \, x^{2} e^{8} \log \left (\frac {5}{3}\right )^{4}}{e^{8} \log \left (\frac {5}{3}\right )^{4} \log \relax (x)^{2} - 2 \, e^{4} \log \left (\frac {5}{3}\right )^{2} \log \relax (x) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.47, size = 564, normalized size = 25.64 \begin {gather*} \frac {3 \, x^{2} e^{8} \log \relax (5)^{4}}{e^{8} \log \relax (5)^{4} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5)^{3} \log \relax (3) \log \relax (x)^{2} + 6 \, e^{8} \log \relax (5)^{2} \log \relax (3)^{2} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5) \log \relax (3)^{3} \log \relax (x)^{2} + e^{8} \log \relax (3)^{4} \log \relax (x)^{2} - 2 \, e^{4} \log \relax (5)^{2} \log \relax (x) + 4 \, e^{4} \log \relax (5) \log \relax (3) \log \relax (x) - 2 \, e^{4} \log \relax (3)^{2} \log \relax (x) + 1} - \frac {12 \, x^{2} e^{8} \log \relax (5)^{3} \log \relax (3)}{e^{8} \log \relax (5)^{4} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5)^{3} \log \relax (3) \log \relax (x)^{2} + 6 \, e^{8} \log \relax (5)^{2} \log \relax (3)^{2} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5) \log \relax (3)^{3} \log \relax (x)^{2} + e^{8} \log \relax (3)^{4} \log \relax (x)^{2} - 2 \, e^{4} \log \relax (5)^{2} \log \relax (x) + 4 \, e^{4} \log \relax (5) \log \relax (3) \log \relax (x) - 2 \, e^{4} \log \relax (3)^{2} \log \relax (x) + 1} + \frac {18 \, x^{2} e^{8} \log \relax (5)^{2} \log \relax (3)^{2}}{e^{8} \log \relax (5)^{4} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5)^{3} \log \relax (3) \log \relax (x)^{2} + 6 \, e^{8} \log \relax (5)^{2} \log \relax (3)^{2} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5) \log \relax (3)^{3} \log \relax (x)^{2} + e^{8} \log \relax (3)^{4} \log \relax (x)^{2} - 2 \, e^{4} \log \relax (5)^{2} \log \relax (x) + 4 \, e^{4} \log \relax (5) \log \relax (3) \log \relax (x) - 2 \, e^{4} \log \relax (3)^{2} \log \relax (x) + 1} - \frac {12 \, x^{2} e^{8} \log \relax (5) \log \relax (3)^{3}}{e^{8} \log \relax (5)^{4} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5)^{3} \log \relax (3) \log \relax (x)^{2} + 6 \, e^{8} \log \relax (5)^{2} \log \relax (3)^{2} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5) \log \relax (3)^{3} \log \relax (x)^{2} + e^{8} \log \relax (3)^{4} \log \relax (x)^{2} - 2 \, e^{4} \log \relax (5)^{2} \log \relax (x) + 4 \, e^{4} \log \relax (5) \log \relax (3) \log \relax (x) - 2 \, e^{4} \log \relax (3)^{2} \log \relax (x) + 1} + \frac {3 \, x^{2} e^{8} \log \relax (3)^{4}}{e^{8} \log \relax (5)^{4} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5)^{3} \log \relax (3) \log \relax (x)^{2} + 6 \, e^{8} \log \relax (5)^{2} \log \relax (3)^{2} \log \relax (x)^{2} - 4 \, e^{8} \log \relax (5) \log \relax (3)^{3} \log \relax (x)^{2} + e^{8} \log \relax (3)^{4} \log \relax (x)^{2} - 2 \, e^{4} \log \relax (5)^{2} \log \relax (x) + 4 \, e^{4} \log \relax (5) \log \relax (3) \log \relax (x) - 2 \, e^{4} \log \relax (3)^{2} \log \relax (x) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.40, size = 58, normalized size = 2.64
method | result | size |
norman | \(\frac {3 \,{\mathrm e}^{8} \left (\ln \relax (5)^{4}-4 \ln \relax (5)^{3} \ln \relax (3)+6 \ln \relax (5)^{2} \ln \relax (3)^{2}-4 \ln \relax (5) \ln \relax (3)^{3}+\ln \relax (3)^{4}\right ) x^{2}}{\left (\ln \relax (x ) {\mathrm e}^{4} \ln \left (\frac {5}{3}\right )^{2}-1\right )^{2}}\) | \(58\) |
risch | \(\frac {3 \left (\ln \relax (5)^{4}-4 \ln \relax (5)^{3} \ln \relax (3)+6 \ln \relax (5)^{2} \ln \relax (3)^{2}-4 \ln \relax (5) \ln \relax (3)^{3}+\ln \relax (3)^{4}\right ) x^{2} {\mathrm e}^{8}}{\left (\ln \relax (x ) \ln \relax (5)^{2} {\mathrm e}^{4}-2 \ln \relax (x ) {\mathrm e}^{4} \ln \relax (3) \ln \relax (5)+\ln \relax (x ) {\mathrm e}^{4} \ln \relax (3)^{2}-1\right )^{2}}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.65, size = 102, normalized size = 4.64 \begin {gather*} \frac {3\,x^2\,{\mathrm {e}}^{24}\,{\left (\ln \relax (3)-\ln \relax (5)\right )}^4}{\left ({\mathrm {e}}^{24}\,{\ln \relax (3)}^4+{\mathrm {e}}^{24}\,{\ln \relax (5)}^4+6\,{\mathrm {e}}^{24}\,{\ln \relax (3)}^2\,{\ln \relax (5)}^2-4\,{\mathrm {e}}^{24}\,\ln \relax (3)\,{\ln \relax (5)}^3-4\,{\mathrm {e}}^{24}\,{\ln \relax (3)}^3\,\ln \relax (5)\right )\,{\ln \relax (x)}^2+\left (4\,{\mathrm {e}}^{20}\,\ln \relax (3)\,\ln \relax (5)-2\,{\mathrm {e}}^{20}\,{\ln \relax (5)}^2-2\,{\mathrm {e}}^{20}\,{\ln \relax (3)}^2\right )\,\ln \relax (x)+{\mathrm {e}}^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.40, size = 180, normalized size = 8.18 \begin {gather*} \frac {- 12 x^{2} e^{8} \log {\relax (3 )} \log {\relax (5 )}^{3} - 12 x^{2} e^{8} \log {\relax (3 )}^{3} \log {\relax (5 )} + 3 x^{2} e^{8} \log {\relax (3 )}^{4} + 3 x^{2} e^{8} \log {\relax (5 )}^{4} + 18 x^{2} e^{8} \log {\relax (3 )}^{2} \log {\relax (5 )}^{2}}{\left (- 4 e^{8} \log {\relax (3 )} \log {\relax (5 )}^{3} - 4 e^{8} \log {\relax (3 )}^{3} \log {\relax (5 )} + e^{8} \log {\relax (3 )}^{4} + e^{8} \log {\relax (5 )}^{4} + 6 e^{8} \log {\relax (3 )}^{2} \log {\relax (5 )}^{2}\right ) \log {\relax (x )}^{2} + \left (- 2 e^{4} \log {\relax (5 )}^{2} - 2 e^{4} \log {\relax (3 )}^{2} + 4 e^{4} \log {\relax (3 )} \log {\relax (5 )}\right ) \log {\relax (x )} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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