Optimal. Leaf size=18 \[ 50625 x^2 \log ^2(2)+\log (x)+x \log \left (x^3\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {14, 2332}
\begin {gather*} x \log \left (x^3\right )+50625 x^2 \log ^2(2)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1+3 x+101250 x^2 \log ^2(2)}{x}+\log \left (x^3\right )\right ) \, dx\\ &=\int \frac {1+3 x+101250 x^2 \log ^2(2)}{x} \, dx+\int \log \left (x^3\right ) \, dx\\ &=-3 x+x \log \left (x^3\right )+\int \left (3+\frac {1}{x}+101250 x \log ^2(2)\right ) \, dx\\ &=50625 x^2 \log ^2(2)+\log (x)+x \log \left (x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} 50625 x^2 \log ^2(2)+\log (x)+x \log \left (x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.30, size = 19, normalized size = 1.06
method | result | size |
default | \(x \ln \left (x^{3}\right )+\ln \left (x \right )+50625 x^{2} \ln \left (2\right )^{2}\) | \(19\) |
risch | \(x \ln \left (x^{3}\right )+\ln \left (x \right )+50625 x^{2} \ln \left (2\right )^{2}\) | \(19\) |
norman | \(x \ln \left (x^{3}\right )+\frac {\ln \left (x^{3}\right )}{3}+50625 x^{2} \ln \left (2\right )^{2}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 18, normalized size = 1.00 \begin {gather*} 50625 \, x^{2} \log \left (2\right )^{2} + x \log \left (x^{3}\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 1.17 \begin {gather*} 50625 \, x^{2} \log \left (2\right )^{2} + \frac {1}{3} \, {\left (3 \, x + 1\right )} \log \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 19, normalized size = 1.06 \begin {gather*} 50625 x^{2} \log {\left (2 \right )}^{2} + x \log {\left (x^{3} \right )} + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 18, normalized size = 1.00 \begin {gather*} 50625 \, x^{2} \log \left (2\right )^{2} + x \log \left (x^{3}\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.10, size = 22, normalized size = 1.22 \begin {gather*} \frac {\ln \left (x^3\right )}{3}+50625\,x^2\,{\ln \left (2\right )}^2+x\,\ln \left (x^3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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