Optimal. Leaf size=23 \[ \frac {2}{5} x \left (-2 x^2+\frac {6 (5+x) \log (x)}{x}\right )^2 \]
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Rubi [B] time = 0.18, antiderivative size = 48, normalized size of antiderivative = 2.09, number of steps used = 18, number of rules used = 8, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.138, Rules used = {12, 14, 2357, 2295, 2304, 2301, 2296, 2305} \begin {gather*} \frac {8 x^5}{5}-\frac {48}{5} x^3 \log (x)-48 x^2 \log (x)+\frac {72}{5} x \log ^2(x)+144 \log ^2(x)+\frac {360 \log ^2(x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2295
Rule 2296
Rule 2301
Rule 2304
Rule 2305
Rule 2357
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-240 x^3-48 x^4+40 x^6+\left (3600+1440 x+144 x^2-480 x^3-144 x^4\right ) \log (x)+\left (-1800+72 x^2\right ) \log ^2(x)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (8 x \left (-30-6 x+5 x^3\right )-\frac {48 \left (-75-30 x-3 x^2+10 x^3+3 x^4\right ) \log (x)}{x^2}+\frac {72 (-5+x) (5+x) \log ^2(x)}{x^2}\right ) \, dx\\ &=\frac {8}{5} \int x \left (-30-6 x+5 x^3\right ) \, dx-\frac {48}{5} \int \frac {\left (-75-30 x-3 x^2+10 x^3+3 x^4\right ) \log (x)}{x^2} \, dx+\frac {72}{5} \int \frac {(-5+x) (5+x) \log ^2(x)}{x^2} \, dx\\ &=\frac {8}{5} \int \left (-30 x-6 x^2+5 x^4\right ) \, dx-\frac {48}{5} \int \left (-3 \log (x)-\frac {75 \log (x)}{x^2}-\frac {30 \log (x)}{x}+10 x \log (x)+3 x^2 \log (x)\right ) \, dx+\frac {72}{5} \int \left (\log ^2(x)-\frac {25 \log ^2(x)}{x^2}\right ) \, dx\\ &=-24 x^2-\frac {16 x^3}{5}+\frac {8 x^5}{5}+\frac {72}{5} \int \log ^2(x) \, dx+\frac {144}{5} \int \log (x) \, dx-\frac {144}{5} \int x^2 \log (x) \, dx-96 \int x \log (x) \, dx+288 \int \frac {\log (x)}{x} \, dx-360 \int \frac {\log ^2(x)}{x^2} \, dx+720 \int \frac {\log (x)}{x^2} \, dx\\ &=-\frac {720}{x}-\frac {144 x}{5}+\frac {8 x^5}{5}-\frac {720 \log (x)}{x}+\frac {144}{5} x \log (x)-48 x^2 \log (x)-\frac {48}{5} x^3 \log (x)+144 \log ^2(x)+\frac {360 \log ^2(x)}{x}+\frac {72}{5} x \log ^2(x)-\frac {144}{5} \int \log (x) \, dx-720 \int \frac {\log (x)}{x^2} \, dx\\ &=\frac {8 x^5}{5}-48 x^2 \log (x)-\frac {48}{5} x^3 \log (x)+144 \log ^2(x)+\frac {360 \log ^2(x)}{x}+\frac {72}{5} x \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 48, normalized size = 2.09 \begin {gather*} \frac {8 x^5}{5}-48 x^2 \log (x)-\frac {48}{5} x^3 \log (x)+144 \log ^2(x)+\frac {360 \log ^2(x)}{x}+\frac {72}{5} x \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.07, size = 36, normalized size = 1.57 \begin {gather*} \frac {8 \, {\left (x^{6} + 9 \, {\left (x^{2} + 10 \, x + 25\right )} \log \relax (x)^{2} - 6 \, {\left (x^{4} + 5 \, x^{3}\right )} \log \relax (x)\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 33, normalized size = 1.43 \begin {gather*} \frac {8}{5} \, x^{5} + \frac {72}{5} \, {\left (x + \frac {25}{x} + 10\right )} \log \relax (x)^{2} - \frac {48}{5} \, {\left (x^{3} + 5 \, x^{2}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 39, normalized size = 1.70
method | result | size |
risch | \(\frac {72 \left (x^{2}+10 x +25\right ) \ln \relax (x )^{2}}{5 x}+\frac {\left (-48 x^{3}-240 x^{2}\right ) \ln \relax (x )}{5}+\frac {8 x^{5}}{5}\) | \(39\) |
default | \(\frac {8 x^{5}}{5}-\frac {48 x^{3} \ln \relax (x )}{5}+\frac {72 x \ln \relax (x )^{2}}{5}-48 x^{2} \ln \relax (x )+\frac {360 \ln \relax (x )^{2}}{x}+144 \ln \relax (x )^{2}\) | \(43\) |
norman | \(\frac {\frac {8 x^{6}}{5}+360 \ln \relax (x )^{2}+144 x \ln \relax (x )^{2}+\frac {72 x^{2} \ln \relax (x )^{2}}{5}-48 x^{3} \ln \relax (x )-\frac {48 x^{4} \ln \relax (x )}{5}}{x}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.35, size = 74, normalized size = 3.22 \begin {gather*} \frac {8}{5} \, x^{5} - \frac {48}{5} \, x^{3} \log \relax (x) - 48 \, x^{2} \log \relax (x) + \frac {72}{5} \, {\left (\log \relax (x)^{2} - 2 \, \log \relax (x) + 2\right )} x + \frac {144}{5} \, x \log \relax (x) + 144 \, \log \relax (x)^{2} - \frac {144}{5} \, x + \frac {360 \, {\left (\log \relax (x)^{2} + 2 \, \log \relax (x) + 2\right )}}{x} - \frac {720 \, \log \relax (x)}{x} - \frac {720}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.11, size = 22, normalized size = 0.96 \begin {gather*} \frac {8\,{\left (15\,\ln \relax (x)+3\,x\,\ln \relax (x)-x^3\right )}^2}{5\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 41, normalized size = 1.78 \begin {gather*} \frac {8 x^{5}}{5} + \left (- \frac {48 x^{3}}{5} - 48 x^{2}\right ) \log {\relax (x )} + \frac {\left (72 x^{2} + 720 x + 1800\right ) \log {\relax (x )}^{2}}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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