Optimal. Leaf size=22 \[ -9-\left (-4+e^3\right )^2-x^2-\frac {3}{\log ^2(x)} \]
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Rubi [A] time = 0.11, antiderivative size = 12, normalized size of antiderivative = 0.55, number of steps used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {6688, 2302, 30} \begin {gather*} -x^2-\frac {3}{\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 x+\frac {6}{x \log ^3(x)}\right ) \, dx\\ &=-x^2+6 \int \frac {1}{x \log ^3(x)} \, dx\\ &=-x^2+6 \operatorname {Subst}\left (\int \frac {1}{x^3} \, dx,x,\log (x)\right )\\ &=-x^2-\frac {3}{\log ^2(x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.55 \begin {gather*} -x^2-\frac {3}{\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 16, normalized size = 0.73 \begin {gather*} -\frac {x^{2} \log \relax (x)^{2} + 3}{\log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 12, normalized size = 0.55 \begin {gather*} -x^{2} - \frac {3}{\log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 13, normalized size = 0.59
method | result | size |
default | \(-x^{2}-\frac {3}{\ln \relax (x )^{2}}\) | \(13\) |
risch | \(-x^{2}-\frac {3}{\ln \relax (x )^{2}}\) | \(13\) |
norman | \(\frac {-3-x^{2} \ln \relax (x )^{2}}{\ln \relax (x )^{2}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 12, normalized size = 0.55 \begin {gather*} -x^{2} - \frac {3}{\log \relax (x)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.26, size = 12, normalized size = 0.55 \begin {gather*} -\frac {3}{{\ln \relax (x)}^2}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 10, normalized size = 0.45 \begin {gather*} - x^{2} - \frac {3}{\log {\relax (x )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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