Optimal. Leaf size=20 \[ x+x^3+\frac {1}{4} (5+x)^4 \log \left (\frac {25}{x^3}\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 5, integrand size = 53, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {12, 14, 32, 2313, 43} \begin {gather*} x^3+\frac {1}{4} (x+5)^4 \log \left (\frac {25}{x^3}\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 32
Rule 43
Rule 2313
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {-1875-1496 x-450 x^2-48 x^3-3 x^4+\left (500 x+300 x^2+60 x^3+4 x^4\right ) \log \left (\frac {25}{x^3}\right )}{x} \, dx\\ &=\frac {1}{4} \int \left (\frac {-1875-1496 x-450 x^2-48 x^3-3 x^4}{x}+4 (5+x)^3 \log \left (\frac {25}{x^3}\right )\right ) \, dx\\ &=\frac {1}{4} \int \frac {-1875-1496 x-450 x^2-48 x^3-3 x^4}{x} \, dx+\int (5+x)^3 \log \left (\frac {25}{x^3}\right ) \, dx\\ &=\frac {1}{4} (5+x)^4 \log \left (\frac {25}{x^3}\right )+\frac {1}{4} \int \left (-1496-\frac {1875}{x}-450 x-48 x^2-3 x^3\right ) \, dx+3 \int \frac {(5+x)^4}{4 x} \, dx\\ &=-374 x-\frac {225 x^2}{4}-4 x^3-\frac {3 x^4}{16}+\frac {1}{4} (5+x)^4 \log \left (\frac {25}{x^3}\right )-\frac {1875 \log (x)}{4}+\frac {3}{4} \int \frac {(5+x)^4}{x} \, dx\\ &=-374 x-\frac {225 x^2}{4}-4 x^3-\frac {3 x^4}{16}+\frac {1}{4} (5+x)^4 \log \left (\frac {25}{x^3}\right )-\frac {1875 \log (x)}{4}+\frac {3}{4} \int \left (500+\frac {625}{x}+150 x+20 x^2+x^3\right ) \, dx\\ &=x+x^3+\frac {1}{4} (5+x)^4 \log \left (\frac {25}{x^3}\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 57, normalized size = 2.85 \begin {gather*} x+x^3+125 x \log \left (\frac {25}{x^3}\right )+\frac {75}{2} x^2 \log \left (\frac {25}{x^3}\right )+5 x^3 \log \left (\frac {25}{x^3}\right )+\frac {1}{4} x^4 \log \left (\frac {25}{x^3}\right )-\frac {1875 \log (x)}{4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 31, normalized size = 1.55 \begin {gather*} x^{3} + \frac {1}{4} \, {\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + 625\right )} \log \left (\frac {25}{x^{3}}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 34, normalized size = 1.70 \begin {gather*} x^{3} + \frac {1}{4} \, {\left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x\right )} \log \left (\frac {25}{x^{3}}\right ) + x - \frac {1875}{4} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 35, normalized size = 1.75
method | result | size |
risch | \(\frac {\left (x^{4}+20 x^{3}+150 x^{2}+500 x \right ) \ln \left (\frac {25}{x^{3}}\right )}{4}+x^{3}+x -\frac {1875 \ln \relax (x )}{4}\) | \(35\) |
norman | \(x +x^{3}+125 \ln \left (\frac {25}{x^{3}}\right ) x +\frac {75 \ln \left (\frac {25}{x^{3}}\right ) x^{2}}{2}+5 \ln \left (\frac {25}{x^{3}}\right ) x^{3}+\frac {\ln \left (\frac {25}{x^{3}}\right ) x^{4}}{4}-\frac {1875 \ln \relax (x )}{4}\) | \(52\) |
derivativedivides | \(\frac {1875 \ln \left (\frac {1}{x}\right )}{4}+x^{3}+x +75 x^{2} \ln \relax (5)+10 x^{3} \ln \relax (5)+\frac {x^{4} \ln \relax (5)}{2}+250 x \ln \relax (5)+\frac {75 x^{2} \ln \left (\frac {1}{x^{3}}\right )}{2}+5 x^{3} \ln \left (\frac {1}{x^{3}}\right )+\frac {x^{4} \ln \left (\frac {1}{x^{3}}\right )}{4}+125 x \ln \left (\frac {1}{x^{3}}\right )\) | \(72\) |
default | \(\frac {1875 \ln \left (\frac {1}{x}\right )}{4}+x^{3}+x +75 x^{2} \ln \relax (5)+10 x^{3} \ln \relax (5)+\frac {x^{4} \ln \relax (5)}{2}+250 x \ln \relax (5)+\frac {75 x^{2} \ln \left (\frac {1}{x^{3}}\right )}{2}+5 x^{3} \ln \left (\frac {1}{x^{3}}\right )+\frac {x^{4} \ln \left (\frac {1}{x^{3}}\right )}{4}+125 x \ln \left (\frac {1}{x^{3}}\right )\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 51, normalized size = 2.55 \begin {gather*} \frac {1}{4} \, x^{4} \log \left (\frac {25}{x^{3}}\right ) + 5 \, x^{3} \log \left (\frac {25}{x^{3}}\right ) + x^{3} + \frac {75}{2} \, x^{2} \log \left (\frac {25}{x^{3}}\right ) + 125 \, x \log \left (\frac {25}{x^{3}}\right ) + x - \frac {1875}{4} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.17, size = 55, normalized size = 2.75 \begin {gather*} \frac {625\,\ln \left (\frac {1}{x^3}\right )}{4}+x\,\left (125\,\ln \left (\frac {25}{x^3}\right )+1\right )+x^3\,\left (5\,\ln \left (\frac {25}{x^3}\right )+1\right )+\frac {75\,x^2\,\ln \left (\frac {25}{x^3}\right )}{2}+\frac {x^4\,\ln \left (\frac {25}{x^3}\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 37, normalized size = 1.85 \begin {gather*} x^{3} + x + \left (\frac {x^{4}}{4} + 5 x^{3} + \frac {75 x^{2}}{2} + 125 x\right ) \log {\left (\frac {25}{x^{3}} \right )} - \frac {1875 \log {\relax (x )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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