Optimal. Leaf size=22 \[ 2+\left (-\frac {5}{x}+x\right )^2-4 \log (2)+\frac {5 x}{\log (27)} \]
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Rubi [A]
time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.18, number of steps
used = 3, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14}
\begin {gather*} \frac {25}{x^2}+\frac {x^2 \log (729)}{2 \log (27)}+\frac {5 x}{\log (27)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {5 x^3+\left (-50+2 x^4\right ) \log (27)}{x^3} \, dx}{\log (27)}\\ &=\frac {\int \left (5-\frac {50 \log (27)}{x^3}+x \log (729)\right ) \, dx}{\log (27)}\\ &=\frac {25}{x^2}+\frac {5 x}{\log (27)}+\frac {x^2 \log (729)}{2 \log (27)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 0.73 \begin {gather*} \frac {25}{x^2}+x^2+\frac {5 x}{\log (27)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 25, normalized size = 1.14
method | result | size |
risch | \(\frac {5 x}{3 \ln \left (3\right )}+x^{2}+\frac {25}{x^{2}}\) | \(17\) |
norman | \(\frac {25+x^{4}+\frac {5 x^{3}}{3 \ln \left (3\right )}}{x^{2}}\) | \(19\) |
default | \(\frac {5 x +3 x^{2} \ln \left (3\right )+\frac {75 \ln \left (3\right )}{x^{2}}}{3 \ln \left (3\right )}\) | \(25\) |
gosper | \(\frac {3 x^{4} \ln \left (3\right )+5 x^{3}+75 \ln \left (3\right )}{3 \ln \left (3\right ) x^{2}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 24, normalized size = 1.09 \begin {gather*} \frac {3 \, x^{2} \log \left (3\right ) + 5 \, x + \frac {75 \, \log \left (3\right )}{x^{2}}}{3 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 24, normalized size = 1.09 \begin {gather*} \frac {5 \, x^{3} + 3 \, {\left (x^{4} + 25\right )} \log \left (3\right )}{3 \, x^{2} \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 24, normalized size = 1.09 \begin {gather*} \frac {3 x^{2} \log {\left (3 \right )} + 5 x + \frac {75 \log {\left (3 \right )}}{x^{2}}}{3 \log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 24, normalized size = 1.09 \begin {gather*} \frac {3 \, x^{2} \log \left (3\right ) + 5 \, x + \frac {75 \, \log \left (3\right )}{x^{2}}}{3 \, \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.45, size = 16, normalized size = 0.73 \begin {gather*} \frac {5\,x}{3\,\ln \left (3\right )}+\frac {25}{x^2}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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