Optimal. Leaf size=14 \[ \left ((20-x)^2-\log (x)\right )^2 \]
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Rubi [B] time = 0.06, antiderivative size = 37, normalized size of antiderivative = 2.64, number of steps used = 9, number of rules used = 6, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.162, Rules used = {14, 893, 2357, 2295, 2301, 2304} \begin {gather*} x^4-80 x^3+2400 x^2-2 x^2 \log (x)-32000 x+\log ^2(x)+80 x \log (x)-800 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 893
Rule 2295
Rule 2301
Rule 2304
Rule 2357
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 (-20+x)^2 \left (-1-40 x+2 x^2\right )}{x}-\frac {2 \left (-1-40 x+2 x^2\right ) \log (x)}{x}\right ) \, dx\\ &=2 \int \frac {(-20+x)^2 \left (-1-40 x+2 x^2\right )}{x} \, dx-2 \int \frac {\left (-1-40 x+2 x^2\right ) \log (x)}{x} \, dx\\ &=2 \int \left (-15960-\frac {400}{x}+2399 x-120 x^2+2 x^3\right ) \, dx-2 \int \left (-40 \log (x)-\frac {\log (x)}{x}+2 x \log (x)\right ) \, dx\\ &=-31920 x+2399 x^2-80 x^3+x^4-800 \log (x)+2 \int \frac {\log (x)}{x} \, dx-4 \int x \log (x) \, dx+80 \int \log (x) \, dx\\ &=-32000 x+2400 x^2-80 x^3+x^4-800 \log (x)+80 x \log (x)-2 x^2 \log (x)+\log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 37, normalized size = 2.64 \begin {gather*} -32000 x+2400 x^2-80 x^3+x^4-800 \log (x)+80 x \log (x)-2 x^2 \log (x)+\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.75, size = 33, normalized size = 2.36 \begin {gather*} x^{4} - 80 \, x^{3} + 2400 \, x^{2} - 2 \, {\left (x^{2} - 40 \, x + 400\right )} \log \relax (x) + \log \relax (x)^{2} - 32000 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.26, size = 36, normalized size = 2.57 \begin {gather*} x^{4} - 80 \, x^{3} + 2400 \, x^{2} - 2 \, {\left (x^{2} - 40 \, x\right )} \log \relax (x) + \log \relax (x)^{2} - 32000 \, x - 800 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 38, normalized size = 2.71
method | result | size |
default | \(x^{4}-2 x^{2} \ln \relax (x )+2400 x^{2}-80 x^{3}+80 x \ln \relax (x )-32000 x +\ln \relax (x )^{2}-800 \ln \relax (x )\) | \(38\) |
norman | \(x^{4}-2 x^{2} \ln \relax (x )+2400 x^{2}-80 x^{3}+80 x \ln \relax (x )-32000 x +\ln \relax (x )^{2}-800 \ln \relax (x )\) | \(38\) |
risch | \(\ln \relax (x )^{2}+\left (-2 x^{2}+80 x \right ) \ln \relax (x )+x^{4}-80 x^{3}+2400 x^{2}-32000 x -800 \ln \relax (x )\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.34, size = 37, normalized size = 2.64 \begin {gather*} x^{4} - 80 \, x^{3} - 2 \, x^{2} \log \relax (x) + 2400 \, x^{2} + 80 \, x \log \relax (x) + \log \relax (x)^{2} - 32000 \, x - 800 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.63, size = 24, normalized size = 1.71 \begin {gather*} \left (40\,x+\ln \relax (x)-x^2\right )\,\left (40\,x+\ln \relax (x)-x^2-800\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.13, size = 37, normalized size = 2.64 \begin {gather*} x^{4} - 80 x^{3} + 2400 x^{2} - 32000 x + \left (- 2 x^{2} + 80 x\right ) \log {\relax (x )} + \log {\relax (x )}^{2} - 800 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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