Optimal. Leaf size=28 \[ 4-e^{5 \left (2+\log \left (x^2\right )\right )}-\frac {4}{x^2}-x+\frac {\log (x)}{x} \]
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Rubi [A] time = 0.03, antiderivative size = 23, normalized size of antiderivative = 0.82, number of steps used = 5, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {14, 2304} \begin {gather*} -e^{10} x^{10}-\frac {4}{x^2}-x+\frac {\log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {8+x-x^3-10 e^{10} x^{12}}{x^3}-\frac {\log (x)}{x^2}\right ) \, dx\\ &=\int \frac {8+x-x^3-10 e^{10} x^{12}}{x^3} \, dx-\int \frac {\log (x)}{x^2} \, dx\\ &=\frac {1}{x}+\frac {\log (x)}{x}+\int \left (-1+\frac {8}{x^3}+\frac {1}{x^2}-10 e^{10} x^9\right ) \, dx\\ &=-\frac {4}{x^2}-x-e^{10} x^{10}+\frac {\log (x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 23, normalized size = 0.82 \begin {gather*} -\frac {4}{x^2}-x-e^{10} x^{10}+\frac {\log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 21, normalized size = 0.75 \begin {gather*} -\frac {x^{12} e^{10} + x^{3} - x \log \relax (x) + 4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 21, normalized size = 0.75 \begin {gather*} -\frac {x^{12} e^{10} + x^{3} - x \log \relax (x) + 4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 0.96
method | result | size |
default | \(-{\mathrm e}^{5 \ln \left (x^{2}\right )+10}-x -\frac {4}{x^{2}}+\frac {\ln \relax (x )}{x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 22, normalized size = 0.79 \begin {gather*} -x^{10} e^{10} - x + \frac {\log \relax (x)}{x} - \frac {4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.36, size = 21, normalized size = 0.75 \begin {gather*} \frac {x\,\ln \relax (x)-4}{x^2}-x-x^{10}\,{\mathrm {e}}^{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 17, normalized size = 0.61 \begin {gather*} - x^{10} e^{10} - x + \frac {\log {\relax (x )}}{x} - \frac {4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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