Optimal. Leaf size=29 \[ \frac {4 x^2 \left (4+\frac {4}{x}+\frac {4+x^2}{x}\right ) \log (x)}{5 \log (5)} \]
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Rubi [A] time = 0.05, antiderivative size = 38, normalized size of antiderivative = 1.31, number of steps used = 7, number of rules used = 4, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.129, Rules used = {12, 2356, 2295, 2304} \begin {gather*} \frac {4 x^3 \log (x)}{5 \log (5)}+\frac {16 x^2 \log (x)}{5 \log (5)}+\frac {32 x \log (x)}{5 \log (5)} \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 {\int \left (32+16 x+4 x^2+\left (32+32 x+12 x^2\right ) \log (x)\right ) \, dx}{5 \log (5)}\\ &=\frac {32 x}{5 \log (5)}+\frac {8 x^2}{5 \log (5)}+\frac {4 x^3}{15 \log (5)}+\frac {\int \left (32+32 x+12 x^2\right ) \log (x) \, dx}{5 \log (5)}\\ &=\frac {32 x}{5 \log (5)}+\frac {8 x^2}{5 \log (5)}+\frac {4 x^3}{15 \log (5)}+\frac {\int \left (32 \log (x)+32 x \log (x)+12 x^2 \log (x)\right ) \, dx}{5 \log (5)}\\ &=\frac {32 x}{5 \log (5)}+\frac {8 x^2}{5 \log (5)}+\frac {4 x^3}{15 \log (5)}+\frac {12 \int x^2 \log (x) \, dx}{5 \log (5)}+\frac {32 \int \log (x) \, dx}{5 \log (5)}+\frac {32 \int x \log (x) \, dx}{5 \log (5)}\\ &=\frac {32 x \log (x)}{5 \log (5)}+\frac {16 x^2 \log (x)}{5 \log (5)}+\frac {4 x^3 \log (x)}{5 \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 0.93 \begin {gather*} \frac {4 \left (8 x \log (x)+4 x^2 \log (x)+x^3 \log (x)\right )}{5 \log (5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 20, normalized size = 0.69 \begin {gather*} \frac {4 \, {\left (x^{3} + 4 \, x^{2} + 8 \, x\right )} \log \relax (x)}{5 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.80, size = 25, normalized size = 0.86 \begin {gather*} \frac {4 \, {\left (x^{3} \log \relax (x) + 4 \, x^{2} \log \relax (x) + 8 \, x \log \relax (x)\right )}}{5 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 23, normalized size = 0.79
method | result | size |
risch | \(\frac {\left (4 x^{3}+16 x^{2}+32 x \right ) \ln \relax (x )}{5 \ln \relax (5)}\) | \(23\) |
default | \(\frac {4 x^{3} \ln \relax (x )+16 x^{2} \ln \relax (x )+32 x \ln \relax (x )}{5 \ln \relax (5)}\) | \(27\) |
norman | \(\frac {32 x \ln \relax (x )}{5 \ln \relax (5)}+\frac {16 x^{2} \ln \relax (x )}{5 \ln \relax (5)}+\frac {4 x^{3} \ln \relax (x )}{5 \ln \relax (5)}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 20, normalized size = 0.69 \begin {gather*} \frac {4 \, {\left (x^{3} + 4 \, x^{2} + 8 \, x\right )} \log \relax (x)}{5 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.27, size = 31, normalized size = 1.07 \begin {gather*} \frac {32\,x^2\,\ln \relax (x)+16\,x^3\,\ln \relax (x)+4\,x^4\,\ln \relax (x)}{5\,x\,\ln \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 20, normalized size = 0.69 \begin {gather*} \frac {\left (4 x^{3} + 16 x^{2} + 32 x\right ) \log {\relax (x )}}{5 \log {\relax (5 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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