Optimal. Leaf size=9 \[ \frac {480 x^3}{\log ^2(x)} \]
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Rubi [C] time = 0.23, antiderivative size = 93, normalized size of antiderivative = 10.33, number of steps used = 11, number of rules used = 6, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2561, 2306, 2309, 2178, 2366, 6482} \begin {gather*} 2160 \text {Ei}(3 \log (x))-2160 (2-3 \log (x)) \text {Ei}(3 \log (x))-12960 \log (x) \text {Ei}(3 \log (x))+2160 (3 \log (x)+1) \text {Ei}(3 \log (x))+4320 x^3+\frac {240 x^3 (2-3 \log (x))}{\log ^2(x)}-\frac {720 x^3 (3 \log (x)+1)}{\log (x)}+\frac {720 x^3 (2-3 \log (x))}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2178
Rule 2306
Rule 2309
Rule 2366
Rule 2561
Rule 6482
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2 (-960+1440 \log (x))}{\log ^3(x)} \, dx\\ &=-2160 \text {Ei}(3 \log (x)) (2-3 \log (x))+\frac {240 x^3 (2-3 \log (x))}{\log ^2(x)}+\frac {720 x^3 (2-3 \log (x))}{\log (x)}-1440 \int \left (\frac {9 \text {Ei}(3 \log (x))}{2 x}-\frac {x^2 (1+3 \log (x))}{2 \log ^2(x)}\right ) \, dx\\ &=-2160 \text {Ei}(3 \log (x)) (2-3 \log (x))+\frac {240 x^3 (2-3 \log (x))}{\log ^2(x)}+\frac {720 x^3 (2-3 \log (x))}{\log (x)}+720 \int \frac {x^2 (1+3 \log (x))}{\log ^2(x)} \, dx-6480 \int \frac {\text {Ei}(3 \log (x))}{x} \, dx\\ &=-2160 \text {Ei}(3 \log (x)) (2-3 \log (x))+\frac {240 x^3 (2-3 \log (x))}{\log ^2(x)}+\frac {720 x^3 (2-3 \log (x))}{\log (x)}+2160 \text {Ei}(3 \log (x)) (1+3 \log (x))-\frac {720 x^3 (1+3 \log (x))}{\log (x)}-2160 \int \left (\frac {3 \text {Ei}(3 \log (x))}{x}-\frac {x^2}{\log (x)}\right ) \, dx-6480 \operatorname {Subst}(\int \text {Ei}(3 x) \, dx,x,\log (x))\\ &=2160 x^3-2160 \text {Ei}(3 \log (x)) (2-3 \log (x))+\frac {240 x^3 (2-3 \log (x))}{\log ^2(x)}+\frac {720 x^3 (2-3 \log (x))}{\log (x)}-6480 \text {Ei}(3 \log (x)) \log (x)+2160 \text {Ei}(3 \log (x)) (1+3 \log (x))-\frac {720 x^3 (1+3 \log (x))}{\log (x)}+2160 \int \frac {x^2}{\log (x)} \, dx-6480 \int \frac {\text {Ei}(3 \log (x))}{x} \, dx\\ &=2160 x^3-2160 \text {Ei}(3 \log (x)) (2-3 \log (x))+\frac {240 x^3 (2-3 \log (x))}{\log ^2(x)}+\frac {720 x^3 (2-3 \log (x))}{\log (x)}-6480 \text {Ei}(3 \log (x)) \log (x)+2160 \text {Ei}(3 \log (x)) (1+3 \log (x))-\frac {720 x^3 (1+3 \log (x))}{\log (x)}+2160 \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-6480 \operatorname {Subst}(\int \text {Ei}(3 x) \, dx,x,\log (x))\\ &=4320 x^3+2160 \text {Ei}(3 \log (x))-2160 \text {Ei}(3 \log (x)) (2-3 \log (x))+\frac {240 x^3 (2-3 \log (x))}{\log ^2(x)}+\frac {720 x^3 (2-3 \log (x))}{\log (x)}-12960 \text {Ei}(3 \log (x)) \log (x)+2160 \text {Ei}(3 \log (x)) (1+3 \log (x))-\frac {720 x^3 (1+3 \log (x))}{\log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 9, normalized size = 1.00 \begin {gather*} \frac {480 x^3}{\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 9, normalized size = 1.00 \begin {gather*} \frac {480 \, x^{3}}{\log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 9, normalized size = 1.00 \begin {gather*} \frac {480 \, x^{3}}{\log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 1.11
method | result | size |
default | \(\frac {480 x^{3}}{\ln \relax (x )^{2}}\) | \(10\) |
norman | \(\frac {480 x^{3}}{\ln \relax (x )^{2}}\) | \(10\) |
risch | \(\frac {480 x^{3}}{\ln \relax (x )^{2}}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.38, size = 17, normalized size = 1.89 \begin {gather*} 4320 \, \Gamma \left (-1, -3 \, \log \relax (x)\right ) + 8640 \, \Gamma \left (-2, -3 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.91, size = 9, normalized size = 1.00 \begin {gather*} \frac {480\,x^3}{{\ln \relax (x)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.89 \begin {gather*} \frac {480 x^{3}}{\log {\relax (x )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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