Optimal. Leaf size=22 \[ -e^4-x^2-\frac {5 (1-\log (x))}{x} \]
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Rubi [A] time = 0.02, antiderivative size = 18, normalized size of antiderivative = 0.82, number of steps used = 5, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {14, 2304} \begin {gather*} -x^2-\frac {5}{x}+\frac {5 \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 {2 \left (-5+x^3\right )}{x^2}-\frac {5 \log (x)}{x^2}\right ) \, dx\\ &=-\left (2 \int \frac {-5+x^3}{x^2} \, dx\right )-5 \int \frac {\log (x)}{x^2} \, dx\\ &=\frac {5}{x}+\frac {5 \log (x)}{x}-2 \int \left (-\frac {5}{x^2}+x\right ) \, dx\\ &=-\frac {5}{x}-x^2+\frac {5 \log (x)}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 0.82 \begin {gather*} -\frac {5}{x}-x^2+\frac {5 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 14, normalized size = 0.64 \begin {gather*} -\frac {x^{3} - 5 \, \log \relax (x) + 5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 18, normalized size = 0.82 \begin {gather*} -x^{2} + \frac {5 \, \log \relax (x)}{x} - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 16, normalized size = 0.73
method | result | size |
norman | \(\frac {-5-x^{3}+5 \ln \relax (x )}{x}\) | \(16\) |
default | \(-x^{2}+\frac {5 \ln \relax (x )}{x}-\frac {5}{x}\) | \(19\) |
risch | \(\frac {5 \ln \relax (x )}{x}-\frac {x^{3}+5}{x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 18, normalized size = 0.82 \begin {gather*} -x^{2} + \frac {5 \, \log \relax (x)}{x} - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.43, size = 16, normalized size = 0.73 \begin {gather*} \frac {5\,\ln \relax (x)-5}{x}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.55 \begin {gather*} - x^{2} + \frac {5 \log {\relax (x )}}{x} - \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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