Optimal. Leaf size=25 \[ 2+\frac {10+16 \left (-3+2 (3-x)^2\right )^2 \log (x)}{x} \]
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Rubi [A]
time = 0.12, antiderivative size = 36, normalized size of antiderivative = 1.44, number of steps
used = 10, number of rules used = 4, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14, 2404,
2332, 2341} \begin {gather*} 64 x^3 \log (x)-768 x^2 \log (x)+\frac {10}{x}+3264 x \log (x)-5760 \log (x)+\frac {3600 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2332
Rule 2341
Rule 2404
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 \left (1795-2880 x+1632 x^2-384 x^3+32 x^4\right )}{x^2}+\frac {48 \left (15-12 x+2 x^2\right ) \left (-5-4 x+2 x^2\right ) \log (x)}{x^2}\right ) \, dx\\ &=2 \int \frac {1795-2880 x+1632 x^2-384 x^3+32 x^4}{x^2} \, dx+48 \int \frac {\left (15-12 x+2 x^2\right ) \left (-5-4 x+2 x^2\right ) \log (x)}{x^2} \, dx\\ &=2 \int \left (1632+\frac {1795}{x^2}-\frac {2880}{x}-384 x+32 x^2\right ) \, dx+48 \int \left (68 \log (x)-\frac {75 \log (x)}{x^2}-32 x \log (x)+4 x^2 \log (x)\right ) \, dx\\ &=-\frac {3590}{x}+3264 x-384 x^2+\frac {64 x^3}{3}-5760 \log (x)+192 \int x^2 \log (x) \, dx-1536 \int x \log (x) \, dx+3264 \int \log (x) \, dx-3600 \int \frac {\log (x)}{x^2} \, dx\\ &=\frac {10}{x}-5760 \log (x)+\frac {3600 \log (x)}{x}+3264 x \log (x)-768 x^2 \log (x)+64 x^3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 36, normalized size = 1.44 \begin {gather*} \frac {10}{x}-5760 \log (x)+\frac {3600 \log (x)}{x}+3264 x \log (x)-768 x^2 \log (x)+64 x^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 37, normalized size = 1.48
method | result | size |
default | \(64 x^{3} \ln \left (x \right )-768 x^{2} \ln \left (x \right )+3264 x \ln \left (x \right )+\frac {3600 \ln \left (x \right )}{x}+\frac {10}{x}-5760 \ln \left (x \right )\) | \(37\) |
norman | \(\frac {10-5760 x \ln \left (x \right )+3264 x^{2} \ln \left (x \right )-768 x^{3} \ln \left (x \right )+64 x^{4} \ln \left (x \right )+3600 \ln \left (x \right )}{x}\) | \(37\) |
risch | \(\frac {16 \left (4 x^{4}-48 x^{3}+204 x^{2}+225\right ) \ln \left (x \right )}{x}-\frac {10 \left (576 x \ln \left (x \right )-1\right )}{x}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 36, normalized size = 1.44 \begin {gather*} 64 \, x^{3} \log \left (x\right ) - 768 \, x^{2} \log \left (x\right ) + 3264 \, x \log \left (x\right ) + \frac {3600 \, \log \left (x\right )}{x} + \frac {10}{x} - 5760 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 31, normalized size = 1.24 \begin {gather*} \frac {2 \, {\left (8 \, {\left (4 \, x^{4} - 48 \, x^{3} + 204 \, x^{2} - 360 \, x + 225\right )} \log \left (x\right ) + 5\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 29, normalized size = 1.16 \begin {gather*} - 5760 \log {\left (x \right )} + \frac {\left (64 x^{4} - 768 x^{3} + 3264 x^{2} + 3600\right ) \log {\left (x \right )}}{x} + \frac {10}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 33, normalized size = 1.32 \begin {gather*} 16 \, {\left (4 \, x^{3} - 48 \, x^{2} + 204 \, x + \frac {225}{x}\right )} \log \left (x\right ) + \frac {10}{x} - 5760 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.95, size = 34, normalized size = 1.36 \begin {gather*} 64\,x^3\,\ln \left (x\right )-768\,x^2\,\ln \left (x\right )-5760\,\ln \left (x\right )+3264\,x\,\ln \left (x\right )+\frac {3600\,\ln \left (x\right )+10}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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