Optimal. Leaf size=24 \[ \frac {x+5 x^3 \left (4-x^2-\frac {3}{\log (x)}\right )}{x} \]
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Rubi [A] time = 0.17, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 12, number of rules used = 7, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {6741, 12, 6688, 14, 2306, 2309, 2178} \begin {gather*} -5 x^4+20 x^2-\frac {15 x^2}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2178
Rule 2306
Rule 2309
Rule 6688
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 x \left (3-6 \log (x)+8 \log ^2(x)-4 x^2 \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=5 \int \frac {x \left (3-6 \log (x)+8 \log ^2(x)-4 x^2 \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=5 \int x \left (8-4 x^2+\frac {3}{\log ^2(x)}-\frac {6}{\log (x)}\right ) \, dx\\ &=5 \int \left (-4 x \left (-2+x^2\right )+\frac {3 x}{\log ^2(x)}-\frac {6 x}{\log (x)}\right ) \, dx\\ &=15 \int \frac {x}{\log ^2(x)} \, dx-20 \int x \left (-2+x^2\right ) \, dx-30 \int \frac {x}{\log (x)} \, dx\\ &=-\frac {15 x^2}{\log (x)}-20 \int \left (-2 x+x^3\right ) \, dx+30 \int \frac {x}{\log (x)} \, dx-30 \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=20 x^2-5 x^4-30 \text {Ei}(2 \log (x))-\frac {15 x^2}{\log (x)}+30 \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=20 x^2-5 x^4-\frac {15 x^2}{\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.83 \begin {gather*} 20 x^2-5 x^4-\frac {15 x^2}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 24, normalized size = 1.00 \begin {gather*} -\frac {5 \, {\left (3 \, x^{2} + {\left (x^{4} - 4 \, x^{2}\right )} \log \relax (x)\right )}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 20, normalized size = 0.83 \begin {gather*} -5 \, x^{4} + 20 \, x^{2} - \frac {15 \, x^{2}}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 0.88
method | result | size |
default | \(-5 x^{4}+20 x^{2}-\frac {15 x^{2}}{\ln \relax (x )}\) | \(21\) |
risch | \(-5 x^{4}+20 x^{2}-\frac {15 x^{2}}{\ln \relax (x )}\) | \(21\) |
norman | \(\frac {-15 x^{2}+20 x^{2} \ln \relax (x )-5 x^{4} \ln \relax (x )}{\ln \relax (x )}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.70, size = 26, normalized size = 1.08 \begin {gather*} -5 \, x^{4} + 20 \, x^{2} - 30 \, {\rm Ei}\left (2 \, \log \relax (x)\right ) + 30 \, \Gamma \left (-1, -2 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.68, size = 20, normalized size = 0.83 \begin {gather*} -5\,x^2\,\left (x^2-4\right )-\frac {15\,x^2}{\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 17, normalized size = 0.71 \begin {gather*} - 5 x^{4} + 20 x^{2} - \frac {15 x^{2}}{\log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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