Optimal. Leaf size=30 \[ 2+e^5 \left (e^5-e^{\frac {2}{\log (x)}}\right )-\frac {x}{2}+9 x^2 \]
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Rubi [A] time = 0.33, antiderivative size = 23, normalized size of antiderivative = 0.77, number of steps used = 5, number of rules used = 3, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {12, 6688, 2209} \begin {gather*} 9 x^2-\frac {x}{2}-e^{\frac {2}{\log (x)}+5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {4 e^{5+\frac {2}{\log (x)}}+\left (-x+36 x^2\right ) \log ^2(x)}{x \log ^2(x)} \, dx\\ &=\frac {1}{2} \int \left (-1+36 x+\frac {4 e^{5+\frac {2}{\log (x)}}}{x \log ^2(x)}\right ) \, dx\\ &=-\frac {x}{2}+9 x^2+2 \int \frac {e^{5+\frac {2}{\log (x)}}}{x \log ^2(x)} \, dx\\ &=-\frac {x}{2}+9 x^2+2 \operatorname {Subst}\left (\int \frac {e^{5+\frac {2}{x}}}{x^2} \, dx,x,\log (x)\right )\\ &=-e^{5+\frac {2}{\log (x)}}-\frac {x}{2}+9 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 0.77 \begin {gather*} -e^{5+\frac {2}{\log (x)}}-\frac {x}{2}+9 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 23, normalized size = 0.77 \begin {gather*} 9 \, x^{2} - \frac {1}{2} \, x - e^{\left (\frac {5 \, \log \relax (x) + 2}{\log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 20, normalized size = 0.67 \begin {gather*} 9 \, x^{2} - \frac {1}{2} \, x - e^{\left (\frac {2}{\log \relax (x)} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 21, normalized size = 0.70
method | result | size |
default | \(9 x^{2}-\frac {x}{2}-{\mathrm e}^{5} {\mathrm e}^{\frac {2}{\ln \relax (x )}}\) | \(21\) |
risch | \(9 x^{2}-\frac {x}{2}-{\mathrm e}^{\frac {5 \ln \relax (x )+2}{\ln \relax (x )}}\) | \(24\) |
norman | \(\frac {-\frac {x \ln \relax (x )}{2}+9 x^{2} \ln \relax (x )-{\mathrm e}^{5} \ln \relax (x ) {\mathrm e}^{\frac {2}{\ln \relax (x )}}}{\ln \relax (x )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 20, normalized size = 0.67 \begin {gather*} 9 \, x^{2} - \frac {1}{2} \, x - e^{\left (\frac {2}{\log \relax (x)} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.24, size = 20, normalized size = 0.67 \begin {gather*} 9\,x^2-{\mathrm {e}}^{\frac {2}{\ln \relax (x)}}\,{\mathrm {e}}^5-\frac {x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 17, normalized size = 0.57 \begin {gather*} 9 x^{2} - \frac {x}{2} - e^{5} e^{\frac {2}{\log {\relax (x )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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