Optimal. Leaf size=28 \[ x-6 x^2 \left (-x+\left (-\frac {-2+\frac {x}{5}}{x}+x\right ) \log (x)\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {12, 2356, 2295, 2304} \begin {gather*} 6 x^3-6 x^3 \log (x)+\frac {6}{5} x^2 \log (x)+x-12 x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2295
Rule 2304
Rule 2356
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (-55+6 x+60 x^2+\left (-60+12 x-90 x^2\right ) \log (x)\right ) \, dx\\ &=-11 x+\frac {3 x^2}{5}+4 x^3+\frac {1}{5} \int \left (-60+12 x-90 x^2\right ) \log (x) \, dx\\ &=-11 x+\frac {3 x^2}{5}+4 x^3+\frac {1}{5} \int \left (-60 \log (x)+12 x \log (x)-90 x^2 \log (x)\right ) \, dx\\ &=-11 x+\frac {3 x^2}{5}+4 x^3+\frac {12}{5} \int x \log (x) \, dx-12 \int \log (x) \, dx-18 \int x^2 \log (x) \, dx\\ &=x+6 x^3-12 x \log (x)+\frac {6}{5} x^2 \log (x)-6 x^3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.00 \begin {gather*} x+6 x^3-12 x \log (x)+\frac {6}{5} x^2 \log (x)-6 x^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 25, normalized size = 0.89 \begin {gather*} 6 \, x^{3} - \frac {6}{5} \, {\left (5 \, x^{3} - x^{2} + 10 \, x\right )} \log \relax (x) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 26, normalized size = 0.93 \begin {gather*} -6 \, x^{3} \log \relax (x) + 6 \, x^{3} + \frac {6}{5} \, x^{2} \log \relax (x) - 12 \, x \log \relax (x) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 26, normalized size = 0.93
method | result | size |
risch | \(\frac {\left (-30 x^{3}+6 x^{2}-60 x \right ) \ln \relax (x )}{5}+6 x^{3}+x\) | \(26\) |
default | \(x +6 x^{3}-6 x^{3} \ln \relax (x )+\frac {6 x^{2} \ln \relax (x )}{5}-12 x \ln \relax (x )\) | \(27\) |
norman | \(x +6 x^{3}-6 x^{3} \ln \relax (x )+\frac {6 x^{2} \ln \relax (x )}{5}-12 x \ln \relax (x )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 25, normalized size = 0.89 \begin {gather*} 6 \, x^{3} - \frac {6}{5} \, {\left (5 \, x^{3} - x^{2} + 10 \, x\right )} \log \relax (x) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.45, size = 26, normalized size = 0.93 \begin {gather*} \frac {x\,\left (6\,x\,\ln \relax (x)-30\,x^2\,\ln \relax (x)-60\,\ln \relax (x)+30\,x^2+5\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 24, normalized size = 0.86 \begin {gather*} 6 x^{3} + x + \left (- 6 x^{3} + \frac {6 x^{2}}{5} - 12 x\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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